user7548: I have problems meditating in the morning. I usually feel very tired when getting up early on a weekday and then have a limited timeframe (~ 30 min.) for meditation.
My body feels so tired, that I am unable to meditate. This is often accompanied by the tendency to get into a negative, rejecting mindstate.
Should I try to meditate anyway or try to bring up energy (going outside, cold shower)? Is it possible to influence the habitual tiredness in the morning (at least a bit), or is this exclusively a body thing?

user-1: Meditation practice in the morning is actually a great time to develop the mind due to the lack of sense stimuli. When we go out in the world the bombardement of sense stimuli begins.
If one is dull in the morning one can splash cold water onto the face or do walking meditation in a brisk tempo immediately followed by sitting meditation. 
One can also make a strong mental resolution to practice or practice sitting meditation with eyes open for a while. There are different ways to arouse the energy faculty. 
Most important thing is to balance the faculties, i.e. to balance Concentration (Samādhi) with Energy (Viriya) and Wisdom (Paññā) with Faith (Saddha).
For information on how to overcome the Hindrances I would recommend the book "The Five Mental Hindrances and Their Conquest" by Nyanaponika Thera.

Is it possible to influence the habitual tiredness in the morning? 

Yes it is. When one is practicing the Dhamma one is training ones mind to overcome and change unwholesome habit patterns of the mind. When practicing meditation intensively one will come to realize that the mind inclines towards whatever is practiced consistently and persistently. 
If one is constantly reacting to e.g. fear, then one will naturally gives rise to more fear in ones life. If one is practicing diligently to overcome unwholesome habits then the mind will incline towards that direction. This is the fantastic thing about the mind that one can mould it in a wholesome direction by practicing the Dhamma. In the end that results in the winning on Nibbana - the issuing of liberation from the rounds of suffering.
Hope this helps. Have a fruitful practice.

user985: I have problems meditating in the morning. I usually feel very tired when getting up early on a weekday and then have a limited timeframe (~ 30 min.) for meditation. My body feels so tired, that I am unable to meditate. This is often accompanied by the tendency to get into a negative, rejecting mindstate.
Life is a Mind-Body phenomenon wherein the six senses are continuously coming in contact with their objects. Since we all have taken birth, the above process is unavoidable. Mental states affect our bodily states and vice versa. Hence, physical tiredness and negative mental states seem co-related.
An effective way to deal with any problem is Yoniso Manasikara or wise reflection. This applies in conventional sense and also in the ultimate sense. In conventional sense, one tries to go to the root of the problem and then tries to get rid of the underlying causes of the problem. In ultimate sense, one tries to understand Anicca (Impermanence), Dukkha (Source of Suffering) and Anatta (Non Self) on the basis of sensations on the body and then realise that fretting over something that is Impermanent, Source of Suffering and Non Self is futile. Ven Yuttadhammo talks more about cultivating wisdom in this talk.
The Importance of Wise Reflection by Steve Weissman is a nice article. It specifically talks about how to cultivate positive mental states in the morning.

Waking up in the morning
This method is a helpful way to begin the day, as it not only helps us
  to develop compassion but also motivates us to think of how fortunate
  we are, for which we give further advice in the next section. This
  helps to expand our concern from simply ourselves and those we know,
  to feel more connected with people we do not know and the universality
  of dukkha.
Upon waking, reflect deeply on a situation in the world where heavy
  dukkha is occurring. Imagine yourself vividly in such a situation in
  order to empathise with those involved and wish them all compassion
  and loving kindness.
Two suggested phrases to use, when wishing compassion and loving
  kindness, are:
“May _ be able to learn, practise and develop methods, techniques
  and tools of mental development, so that  can cope with,
  understand, accept and overcome the difficulties and challenges of
  life. May  find peace of mind.” “May  be able to let go of
  anger, fear, worry and ignorance. May  also have patience, courage,
  wisdom and determination to meet and overcome difficulties and
  problems, challenges of life. May _ find peace of mind.” 
How fortunate we are
Simply reflect on all the different ways that you are fortunate, materially and mentally. Watch out for the word “but”—it is
  not part of this reflection. This reflection is also very good when
  waking up each morning.
It can be especially helpful to consider the odds of being born human
  compared to being born another being on this planet. Then consider how
  many have the chance to read or listen to the Dhamma. Then consider
  how many have the chance to actually practise the Dhamma. How very,
  very fortunate we are.
To truly understand how fortunate we are is extremely helpful, in
  particular, with letting go of self-pity. This then allows more joy,
  contentment and energy to arise.
Self-pity is a major hindrance for so many meditators. One main reason
  is because they are not looking at themselves objectively and
  truthfully. But in this practice we try to be objective with our view
  of life. We try to see life truly for what it actually is. Thus
  reflecting on how fortunate we are is a very simple and effective
  technique to find more inner peace.

I do not know if the author is suggesting to do loving kindness meditation before reflecting on our fortunes, but I think that counting our fortunes, then sitting meditation and then loving kindness meditation would be the right order. 

user-1: i have hard time meditating right after waking up too.  Perhaps brain was working harder while asleep (dreams etc.) and needed a moment to calm down?   Walking meditation does wonder in this situation.  

user295: How to overcome lethargy in the morning

Walking meditation can help as mentioned in one of the other answers
If you are doing body scanning meditation then do this fast and taking large parts. Fast movement increases vitakka.
If you are doing breath meditation or samatha increase reviewing (see p 35 Knowing and See by Ven. Pa Auk Sayadaw) if the mind is with the object and redirect your attention to the object. This keeps your mind from wandering away.
Also this can be partly due to drowsiness / sloth and torpor hence look at the techniques in: Pacalā Sutta
Work on raising your energy levels. See section below.

Should you meditate at least a little in the morning when you are time pressed and lethargic
You pratice twice a day. Morning session reduces the build up of defilements over nights. Also if in one period the meditation session is full of hindrances at least the other will workout. Do not assume this will always happen in the mornings.
Rise energy levels
Trying to maintain the object of meditation (vitakka & Vicara) itself rises energy levels. Also Right Effort to abandon hindrances and the unwholesome roots (greed (lobha), hatred (dosa) and delusion (moha)) [see Pahāna Sutta for the method] and develop the Enlightenment Factors (especially Joy or rapture (pīti), Investigation (dhamma vicaya) and Energy (viriya)) make you energetic.

user254: There are two descriptions here of the Dalai Lama's morning routine:

Routine Day

When His Holiness is at home in Dharamsala, he wakes up at 3 am. After his morning shower, His Holiness begins the day with prayers, meditations and prostrations until 5 am. From 5 am His Holiness takes a short morning walk around the residential premises. If it is raining outside, His Holiness has a treadmill to use for his walk.


At Home With the Dalai Lama

At 3:45 a.m. ... At a time when only the street dogs were up, the Dalai Lama began his prostrations. ... I lost count after a while, but I figured he must have done about three dozen full prostrations. ... With his prostrations done, he walked to a treadmill tucked away by the window. He hung his prayer beads on the handle bar next to a draped towel and began to pace rapidly on the moving belt. Almost immediately he closed his eyes as he surrendered to the machine's rhythm, and meditated as he exercised. it was a much faster version of walking meditation. ... After showering, the Dalai Lama took me up to the roof of the residence. ... The Dalai Lama stared into the distance, absorbing the quiet, allowing all his senses to experience the tranquil majesty of the surroundings. ... It was chilly and we didn't stay long on the roof. After we returned to his room, the Dalai Lama immediately went into meditation. He sat on a cushion behind his desk ...



Perhaps this indicates how the Dalai Lama awakens his body before and during morning meditation.

7548: <p>I have problems meditating in the morning. I usually feel very tired when getting up early on a weekday and then have a limited timeframe (~ 30 min.) for meditation.</p>

<p>My body feels so tired, that I am unable to meditate. This is often accompanied by the tendency to get into a negative, rejecting mindstate.</p>

<p>Should I try to meditate anyway or try to bring up energy (going outside, cold shower)? Is it possible to influence the habitual tiredness in the morning (at least a bit), or is this exclusively a body thing?</p>
 -1: <p>Meditation practice in the morning is actually a great time to develop the mind due to the lack of sense stimuli. When we go out in the world the bombardement of sense stimuli begins.</p>

<p>If one is dull in the morning one can splash cold water onto the face or do walking meditation in a brisk tempo immediately followed by sitting meditation. </p>

<p>One can also make a strong mental resolution to practice or practice sitting meditation with eyes open for a while. There are different ways to arouse the energy faculty. </p>

<p>Most important thing is to balance the faculties, i.e. to balance <em>Concentration (Samādhi)</em> with <em>Energy (Viriya)</em> and <em>Wisdom (Paññā)</em> with <em>Faith</em> (Saddha).</p>

<p>For information on how to overcome the Hindrances I would recommend the book <a href="http://www.accesstoinsight.org/lib/authors/nyanaponika/wheel026.html" rel="nofollow"><em>"The Five Mental Hindrances and Their Conquest"</em></a> by Nyanaponika Thera.</p>

<blockquote>
  <p>Is it possible to influence the habitual tiredness in the morning? </p>
</blockquote>

<p>Yes it is. When one is practicing the Dhamma one is training ones mind to overcome and change unwholesome habit patterns of the mind. When practicing meditation intensively one will come to realize that the mind inclines towards whatever is practiced consistently and persistently. </p>

<p>If one is constantly reacting to e.g. fear, then one will naturally gives rise to more fear in ones life. If one is practicing diligently to overcome unwholesome habits then the mind will incline towards that direction. This is the fantastic thing about the mind that one can mould it in a wholesome direction by practicing the Dhamma. In the end that results in the winning on Nibbana - the issuing of liberation from the rounds of suffering.</p>

<p>Hope this helps. Have a fruitful practice.</p>
 985: <p><strong>I have problems meditating in the morning. I usually feel very tired when getting up early on a weekday and then have a limited timeframe (~ 30 min.) for meditation. My body feels so tired, that I am unable to meditate. This is often accompanied by the tendency to get into a negative, rejecting mindstate.</strong></p>

<p>Life is a Mind-Body phenomenon wherein the six senses are continuously coming in contact with their objects. Since we all have taken birth, the above process is unavoidable. Mental states affect our bodily states and vice versa. Hence, physical tiredness and negative mental states seem co-related.</p>

<p>An effective way to deal with any problem is <em>Yoniso Manasikara</em> or wise reflection. This applies in conventional sense and also in the ultimate sense. In conventional sense, one tries to go to the root of the problem and then tries to get rid of the underlying causes of the problem. In ultimate sense, one tries to understand <em>Anicca</em> (Impermanence), <em>Dukkha</em> (Source of Suffering) and <em>Anatta</em> (Non Self) on the basis of sensations on the body and then realise that fretting over something that is Impermanent, Source of Suffering and Non Self is futile. Ven Yuttadhammo talks more about cultivating wisdom in this <a href="https://www.youtube.com/watch?v=swrTf6je3Ys" rel="nofollow">talk</a>.</p>

<p><a href="http://www.bps.lk/olib/wh/wh463-p.html#Wakingupinthemorning" rel="nofollow">The Importance of Wise Reflection</a> by Steve Weissman is a nice article. It specifically talks about how to cultivate positive mental states in the morning.</p>

<blockquote>
  <p><strong>Waking up in the morning</strong></p>
  
  <p>This method is a helpful way to begin the day, as it not only helps us
  to develop compassion but also motivates us to think of how fortunate
  we are, for which we give further advice in the next section. This
  helps to expand our concern from simply ourselves and those we know,
  to feel more connected with people we do not know and the universality
  of dukkha.</p>
  
  <p>Upon waking, reflect deeply on a situation in the world where heavy
  dukkha is occurring. Imagine yourself vividly in such a situation in
  order to empathise with those involved and wish them all compassion
  and loving kindness.</p>
  
  <p>Two suggested phrases to use, when wishing compassion and loving
  kindness, are:</p>
  
  <p>“May <strong>_ be able to learn, practise and develop methods, techniques
  and tools of mental development, so that <em></strong> can cope with,
  understand, accept and overcome the difficulties and challenges of
  life. May <strong></em> find peace of mind.” “May <em></strong> be able to let go of
  anger, fear, worry and ignorance. May <strong></em> also have patience, courage,
  wisdom and determination to meet and overcome difficulties and
  problems, challenges of life. May _</strong> find peace of mind.” </p>
  
  <p><strong>How fortunate we are</strong></p>
  
  <p>Simply reflect on all the different ways that you are fortunate, materially and mentally. Watch out for the word “but”—it is
  not part of this reflection. This reflection is also very good when
  waking up each morning.</p>
  
  <p>It can be especially helpful to consider the odds of being born human
  compared to being born another being on this planet. Then consider how
  many have the chance to read or listen to the Dhamma. Then consider
  how many have the chance to actually practise the Dhamma. How very,
  very fortunate we are.</p>
  
  <p>To truly understand how fortunate we are is extremely helpful, in
  particular, with letting go of self-pity. This then allows more joy,
  contentment and energy to arise.</p>
  
  <p>Self-pity is a major hindrance for so many meditators. One main reason
  is because they are not looking at themselves objectively and
  truthfully. But in this practice we try to be objective with our view
  of life. We try to see life truly for what it actually is. Thus
  reflecting on how fortunate we are is a very simple and effective
  technique to find more inner peace.</p>
</blockquote>

<p>I do not know if the author is suggesting to do loving kindness meditation before reflecting on our fortunes, but I think that counting our fortunes, then sitting meditation and then loving kindness meditation would be the right order. </p>
 -1: <p>i have hard time meditating right after waking up too.  Perhaps brain was working harder while asleep (dreams etc.) and needed a moment to calm down?   Walking meditation does wonder in this situation.  </p>
 295: <p><strong>How to overcome lethargy in the morning</strong></p>

<ul>
<li>Walking meditation can help as mentioned in one of the other answers</li>
<li>If you are doing body scanning meditation then do this fast and taking large parts. Fast movement increases <a href="https://en.wikipedia.org/wiki/Vitarka" rel="nofollow noreferrer">vitakka</a>.</li>
<li>If you are doing breath meditation or <a href="https://en.wikipedia.org/wiki/Samatha" rel="nofollow noreferrer">samatha</a> increase reviewing (see p 35 <a href="http://www.dhammatalks.net/Books13/Pa-Auk-Sayadaw_Knowing-and-Seeing-4th-Ed-2010.pdf" rel="nofollow noreferrer">Knowing and See</a> by Ven. Pa Auk Sayadaw) if the mind is with the object and <a href="https://en.wikipedia.org/wiki/Vicara" rel="nofollow noreferrer">redirect your attention to the object</a>. This keeps your mind from wandering away.</li>
<li>Also this can be partly due to drowsiness / <a href="https://en.wikipedia.org/wiki/Thina" rel="nofollow noreferrer">sloth</a> and <a href="https://en.wikipedia.org/wiki/Middha" rel="nofollow noreferrer">torpor</a> hence look at the techniques in: <a href="http://www.themindingcentre.org/dharmafarer/wp-content/uploads/2009/12/4.11-Pacala-S-a7.58-piya.pdf" rel="nofollow noreferrer">Pacalā Sutta</a></li>
<li>Work on raising your energy levels. See section below.</li>
</ul>

<p><strong>Should you meditate at least a little in the morning when you are time pressed and lethargic</strong></p>

<p>You pratice twice a day. Morning session reduces the build up of defilements over nights. Also if in one period the meditation session is full of hindrances at least the other will workout. Do not assume this will always happen in the mornings.</p>

<p><strong>Rise energy levels</strong></p>

<p>Trying to maintain the object of meditation (<a href="https://en.wikipedia.org/wiki/Vitarka" rel="nofollow noreferrer">vitakka</a> &amp; <a href="https://en.wikipedia.org/wiki/Vicara" rel="nofollow noreferrer">Vicara</a>) itself rises energy levels. Also Right Effort to abandon hindrances and the unwholesome roots (greed (lobha), hatred (dosa) and delusion (moha)) [see <a href="http://www.themindingcentre.org/dharmafarer/wp-content/uploads/2010/02/31.1-Pahana-S-s36.3-piya.pdf" rel="nofollow noreferrer">Pahāna Sutta</a> for the method] and develop the <a href="https://en.wikipedia.org/wiki/Seven_Factors_of_Enlightenment" rel="nofollow noreferrer">Enlightenment Factors</a> (especially Joy or rapture (pīti), Investigation (dhamma vicaya) and Energy (viriya)) make you energetic.</p>
 254: <p>There are two descriptions here of the Dalai Lama's morning routine:</p>
<ul>
<li><p><a href="http://dalailama.com/biography/a-routine-day" rel="nofollow noreferrer">Routine Day</a></p>
<blockquote>
<p>When His Holiness is at home in Dharamsala, he wakes up at 3 am. After his morning shower, His Holiness begins the day with prayers, meditations and prostrations until 5 am. From 5 am His Holiness takes a short morning walk around the residential premises. If it is raining outside, His Holiness has a treadmill to use for his walk.</p>
</blockquote>
</li>
<li><p><a href="http://www.huffingtonpost.com/victor-chan/dalai-lama-mindfulness_b_3683961.html" rel="nofollow noreferrer">At Home With the Dalai Lama</a></p>
<blockquote>
<p>At 3:45 a.m. ... At a time when only the street dogs were up, the Dalai Lama began his prostrations. ... I lost count after a while, but I figured he must have done about three dozen full prostrations. ... With his prostrations done, he walked to a treadmill tucked away by the window. He hung his prayer beads on the handle bar next to a draped towel and began to pace rapidly on the moving belt. Almost immediately he closed his eyes as he surrendered to the machine's rhythm, and meditated as he exercised. it was a much faster version of walking meditation. ... After showering, the Dalai Lama took me up to the roof of the residence. ... The Dalai Lama stared into the distance, absorbing the quiet, allowing all his senses to experience the tranquil majesty of the surroundings. ... It was chilly and we didn't stay long on the roof. After we returned to his room, the Dalai Lama immediately went into meditation. He sat on a cushion behind his desk ...</p>
</blockquote>
</li>
</ul>
<p>Perhaps this indicates how the Dalai Lama awakens his body before and during morning meditation.</p>
