Sure, I would like to be able to train a stubborn courser into a spirited courser, or a heavy courser, but no amount of training will ever make a waybacked packhorse (sumpter) into a charger. So maybe just a change of the modifier, or a +1 change in one of the aspects of the horse for each level, up to a limit.
I would like to see armour for the horses. You would add or remove the barding and be able to move faster without it, but have a better charge and armour class for the horse with it. That would also require the horses to have inventory slots, which has been mentioned in other threads, but I see it like this: A rider takes up 5 slots, anything else takes up one slot. From 5 to 7 slots would allow room for just a rider (Riding horse, sumpter horse), a rider and armour, or a rider and a weapon (spare weapon/ammunition/shield), up to a rider, armour, and a spare weapon.
mfberg
sorry for running on at the brain, but tangents go where tangents go