Only short or composite bow allowed while on horseback.
Allow only hardy and heavy varieties.
Unable to change speed or direction of movement while holding bow.
Reduse speed of horse while holding bow (like -30%).
Reduse reloading speed while on horseback (like -40%).
Allow to shoot in 120 degrees infront of horse (unable to shoot backwards).
And *maybe* then it wouldn't be unbalaced.
i would sugest a special horse bow, smaler and with less power than normal bows what would reduce damage and range, the way horse archery was used by de Huns was sprinting for the enemy and shot for short range. they usualy do almost no damage against heavy infantry and are verry weak against other archers, that have a larger target to hit, and ligth cavalry, the slower speed of the horse archer would made him a easy target for a horse swordsman or spearmen, because it would be slower and canot shot back.
another way to win a battle against a horse archer is bring them to the woods, it will be even slower and a spearmen could be able to get them kiled, he may be weak agains trowing weapons too.
another point is that hrse archers canot shot both sides withou change direction of the horse, so a rigth handed warior can only shoot to de left side of the horse, this would limit the ability to shot.
i would sugest too a penalty on acuraçy