You could find some balance if you made one or two bows that were the only bows usable on horseback.
Giving them stats that no footarcher/crossbowman would consider using.
So that if you get unhorsed, the HA/HX would be at a disadvantage.
Without the speedbonus and mobility of your mount you would have poor dmg.
Removing the long range efficiency would be key. Reducing missile speed ,draw speed and accuracy. increasing dmg.
You had to draw your bow and get upclose and personal with the target to make it really sting. Hone riderskills and aggressive play.
The most annoying is to chase HA/HX that ride away from you and pew. Never letting you come close ever.
Disclaimer: I love to HT.
People say that reducing damage won't help. I don't really agree. The less damage, the more armour will help, the less they stagger, the less valour they get and the less of a nuisance they will be. The less of a nuisance, the less QQ, the less the HA gets pleasure from playing the class and we get fewer HA's. I'd put "Can't use on horseback" on all the current bows, but add some HA variants with worse stats. Yumi with adjusted stats that is balanced just for using on a horse that uses 2-3 slots etc. Its realistic because you would draw slower, you probably wouldn't get the full accuracy or draw as far back. Well if its less realistic I don't care either way. Shooting on a horse isn't like shooting from a fixed platform irl. Horses don't spin around so fast etc
Alternatively just add the Can't Use on Horseback stat to Yumi and Horn Bow and increase the slots on arrows to 2. Two birds, one stone..theres way too much ammo on ranged classes as it is, let alone HA's