B737-300
Flight Crew Last 90 Days 234; Flight Crew Type 5000
Aircraft Equipment Problem Critical
Air Traffic Control Issued New Clearance; Flight Crew Overcame Equipment Problem
Aircraft
At the beginning of descent anti-ice was placed on; and thrust was reduced to idle.  The First Officer noticed the air mix valve on right pack going to full cold.  He then noticed that the air mix valve on the left pack going to full hot.  He tried to control the right pack by utilizing manual control with no effect.  I queried if there was perhaps a pack trip although none was indicated.  At that time; the Cabin Altitude Warning Horn sounded.  We immediately donned oxygen masks and established communication.  We initiated a rapid descent to FL200 and requested 10;000 feet with ATC.  That was approved.  We were asked if we required assistance.  I answered in the negative and no emergency was declared.  I did state that we were having difficulty maintaining cabin pressurization and that we would like to be cleared directly to [destination].  That was approved.  We ran the Cabin Altitude Warning/Abnormal Pressurization Checklist followed by the Emergency Descent Checklist.  The passenger oxygen masks did not deploy as the cabin altitude hovered around 12;700 feet and never exceeded 14;000 feet.  At a cabin altitude of 10;000 feet; the masks were removed and we proceeded without further event.
[Narrative 2 had no additional information]
B737-300 flight crew reported loss of cabin pressure in descent; possibly associated with an unannuciated pack trip. Cabin altitude never exceeded 14;000 feet and the flight landed without further incident.