I'm making this suggestion since I haven't seen anyone really flesh out the mechanics of it. Plus, the suggestions I've seen (with the exception of a small mention in a mainly archery based post) have all been shot down as "immediately" OP, which isn't the case. In real life horsebound archery has been a viable hit and run tactic, but comes at the cost of having no hands on the reigns of the animal and as a result, required the horse to be trained completely different. In order to balance this within the game, I feel that having the horse take a turning penalty, as well as a very slight forward movement penalty (5%? Just enough to be able to be chased down if caught out). The rider should obviously have a massive challenge of aiming the bow and reloading, justified as a large penalty to aim and reload speed.
To clarify, I'm not suggesting that archers be allowed to ride warhorses as they are now, but instead be given a specialized variety of horse that can respond to their needs as well as balance them effectively. Heck. a horse capable of responding to commands given without reigns would also be able to hold a rider with a 2h sword, axe, etc.