The actual answer in many cases depends on the time period you're talking about. In some eras the procurement of horses was well done, in others it was not. There were some geographical differences even in the same time period. Eastern regiments were often reported as being better mounted than the Western regiments. Some of this might have been prejudice, as the Army leadership liked the big "American" horse (probably a TB or TB-type) where the Western regiments often were mounted on more "coarse" animals that were, in fact, better suited to the frontier conditions.
You could also start quite a fist fight in the Officer's Mess over what type of horse WAS best suited to the American Cavalry. The best answer was likely "where will I be operating?" But in an organization given to "binary" thinking and remembering that it was the "bean counters" who often had the last say operational logic was not always foremost!!!
As to color, there were color differences by company in at least some of the eras. I ran across a reference from the Dragoon era but lost it. I suspect you could spend some time on Google and get some decent answers.
During the final decades of the Horse Cavalry the Remount Service was established and did standardize the cavalry horse as a TB-type horse, 15-16 hands, 900-1100 pounds. By the time the Phillips Officers Saddle was introduced in 1936 it was produced in only one tree size. That's how consistent the Remount Service was in producing horses. This initiative had a major impact on the U.S. horse market that can be felt today in some breeds and lines.
While the TB-type was officially the preferred Cavalry horse some officers had other preferences. Dr. Kellogg (of Cornflakes fame) had donated an Arabian breeding operation to the Army and many officers like this type of horse. Col Frank Tompkins, author of
Chasing Villa, as a major took two Arabian stallions into Mexico with him. A Morgan breeding program had also been donated to the Army and many Artillery and Infantry officers liked them. But these two breeds were very, very small in relation the TB-type horse that was the standard. In the Remount Service more than 90% of the stallions (which numbered more than 100) were TB or TB-type and some were quite famous in their day.
SQQ