Q:

Horn clefs across two staves

I am not a horn player, but I do have a bit of knowledge about them. Horn parts can be written in the G or F clefs, right? Is it common practice to put the first horn stave (horns 1 and 3) in the G clef and the second stave (2 and 4) in the F clef at the same time? Or is it courtesy to put both in the same clef?

A:

Bob has a lot of good information in his answer. I'll just add abit more here.
As I'm sure you know (but I'll repeat for the sake of others, and for clarity), horn players tend to specialize in either higher parts or lower parts. They are typically notated with one "high" horn and one "low" horn per staff. So you usually have:
Staff One:

Horn I (high) 
Horn II (low)

Staff Two:

Horn III (high)
Horn IV (low)

In fact, it is not at all uncommon for staff 1 to have a high and a low part, and staff 2 to have the exact same high and low part. To me, this seems sort of the opposite of what you'd expect, but it is what it is. As a result of this layout, you might expect that when one staff switches to bass clef (which is pretty rare), it is the low horn that will mostly be playing that part, and the high horn on that staff might not even be playing.
I just flipped through my entire score of Holst's The Planets and found only one instance of horns using the bass clef. It's on the first two pages of Mars, when the main theme is first heard. Holst is using a larger orchestra, with 6 horns, and he has them divided into two staves of 3 horns each: staff 1 has horns I, II, and III, while staff 2 has horns IV, V, and VI. In this passage, the second staff switches to bass clef, and only horns V and VI are instructed to play, in unison (horn IV presumably specializing in higher notes, and not needed to balance with the rest of the orchestra). Technically, staff 1 is still notated in the treble clef at this point, but none of those horns (I, II, III) are actually playing anything here, so its sort of a moot point.
Looking at Norman DelMar's Anatomy of the Orchestra, he discusses the alternate possibility of combining the high horns (I and III) on one staff, and the low horns (II and IV) on another staff. Of this he says:

This kind of shorthand also robs the horn quartet of the stylistic
  character derived from its origin in independent pairs. Moreover the
  2nd and 4th can easily find themselves endlessly rumbling about in the
  depths simply because they have been put together on a single stave in
  the bass clef.

The example he uses to illustrate this point is from Bartok's Dance Suite (bars 90-96), in which I and III are on a staff in the treble clef, and II and IV are on a staff in the bass clef. Unfortunately, I can't find the full score on IMSLP.
On the next page, he says

By far the most usual score layout is for two horns at a time to occupy a stave, and this may persist even when they have different clefs. [emph. mine]

He then gives an inline example with a single pair of notes to show what a staff with two clefs at the same time looks like. I have never seen anything like this before, and did not even know it was possible. Unfortunately, he does not mention any particular work where this is done.
Edit: I just happened to stumble across an example of dual clefs for horns, in Schubert's Great Symphony No. 9, which you can see here, at 12:08, on the 5th staff down from the top. Note that this piece only has two horns, and they are apparently natural (unvalved) horns, so they only get the notes of the harmonic series. Also note that the note in the bass clef uses the older "octave lower" system that Bob mentions. In fact, I believe this note is the horn's fundamental pitch.

A:

Okay, I just pulled out a few scores from my bookcase (looked at some Berlioz, Bartok, Stravinsky and Brahms so far…). In the scores at least, nearly all of the horns are written on two treble (G) clef staves. The scores are all transposing, so I can't see any reason why this wouldn't also be the case for the parts. I do know that horn parts are commonly written with all four parts on two staves in the parts, which is unlike most instruments.
Only the Stravinsky had any bass clef, and this was for really low notes. If you think about it, the strong range of the horn is likely to be fine notated in the treble clef for the majority of the time. The best thing to do is use your common sense; just as when writing for any other instrument that is "borderline" between treble and bass clef (eg. sounding pitch Tenor Sax), use whichever clef is best for any particular passage.
Just a couple of other "interesting" peculiarities about horn parts (sure you might know these already, but hey…) In many scores horn parts have no key signature; they simply have all the accidentals written in. According to my copy of Instrumentation and Orchestration by Alfred Blatter, "When writing horn parts in the bass clef one treats the bass clef in the same manner as is done for piano. (There is an old notation for bass clef notes often found in parts written for historical natural horns; it is written an octave lower than the notation dictated by modern practice and should never be used by a contemporary writer for the horn.) Horn players do not read high notes notated in the bass clef well. Therefore, one should never write notes above G" at the top of the bass clef.
You obviously already know about how to split horns 1-3 and 2-4...

A:

Horns have a very extensive range (From F#2 to C6) so it will depend more on the part itself. If the part is written in the higher range of the horn then a treble clef will be used. If the part is written in the lower range of the horn then a bass clef is used. Typically horns 2 and 4 will play the lower part and if it fits better in bass clef then it should be written in bass clef.

