The riding skill also changes how responsive to your commands the horse is, as well. It'll start up, slow down, turn and stop more quickly, as well as reach a greater top speed. If you know you are soon going to increase your riding skill and want to move up to a warhorse, buy a lame one (it'll cost less than one in good health), keep it in your inventory for about a week, and it'll be healed when you are ready-
Also note that if a spirited or champion horse is lamed in battle, it will heal as well... but it will be a normal horse when healed...
TA