Horse archers were quite a plague in medieval times and it's difficult to have them in this game and not have them either overpowered or artificially nerfed.
I think it would be a nice compromise to give small nerfs to cavalry-compatible bows' damage and horse archers' armor and/or hp (making them more easily countered with foot archers). It would also be a great idea to weaken things like bows/arrows and thrown weapons against heavy armor (I mean, c'mon, one hand-thrown javelin has about as much ballistic force against a fully armored knight as a close-range rifle shot...). Change them to cutting damage maybe? Keep crossbows as piercing damage (they're crossbows after all, praised for their armor-penetrating ability), maybe let arrows provide some piercing bonus based on their quality.