When I wrote my game Fantasy Imperium, I discovered that horses aren't very detailed in most games.
I like the comments above about horses that have a mind of their own. You could incorporate this into your stories by thinking of the horse as another character.
How many players know the names of thier horse?
What i've discovered about horses is that there are many kinds of horses and each have their own perculiarities.
Every breed of horse will have a different set of gaits.
Walk, trot, canter, gallop, are some of these.
Gaits are the different way in which a horse moves. These determine how fast the horse is moving and how well balanced he is.
The natural gaits are walk, trot and gallop. Other types of gaits are inherited by the particular breed of horse or can be trained.
A horse that has been trained to employ certain kinds of gaits will move more efficiently and will give less fatigue to the rider and horse alike.
Suddenly stopping a horse may require a riding skill check.
When using a particular gait, it could bounce the rider around more, and this will affect his ability in combat too.
Horses do not move backward normally, but can be trained to do so.
A special type of gait called, Ambling Gait, has been used for centuries to lessen the rider and horse fatigue over long distances. War horses don't usually have this type of gait.
So when traveling, a knight will not ride his war horse. This expensive horse is trained for combat and could be ruined by simple travel. A knight would probably have a riding horse, and a squire would also ride along to lead the knight's warhorse and to take care of him.
Another thing to consider is that if you get on a horse that has been ridden by someone else, you can notice it, because it will affect the horses movement.
If you try to ride a very good quality horse, but don't have much riding skill, it could ruin the horse. Conversely, if you try to use your excellent riding skill on a poor quality horse, it wont work so well.