The balancing of horse archers is going to be one of the trickiest things Taleworlds tackles during EA.
Pre-1.5 patch, it's safe to say horse archers were sickeningly OP, due to their aim being infallible even at full gallop.
The most recent patches mitigated this by creating an inverse relationship between accuracy and movement speed (as it should be).
The issue now is to what degree should movement speed affect accuracy.
I currently find it fairly balanced, but people are welcome to disagree.
Of course, I'm only looking at this problem through the scope of what I know (A rather myopic and single-minded Skirmish Mode standpoint).
I can't really say how these changes affect Captain Mode or singleplayer, but I imagine they are invariably different from Skirmish.
Why? Because whereas a player knows how much to slow down, how long to draw, and how to lead their shot a certain way, an AI bot (be it in Captain Mode or singleplayer) does not. At the end of the day, they're just a bot. I'd think the rules of horse archery would have to be tweaked or bent depending the game mode or whether it's singleplayer/multiplayer.
This is why balancing horse archers is going to be one of Taleworlds' toughest challenges, because they are going to have to juggle three different systems that are all mutually exclusive from one another in terms of their balances and metas.
I wish you good luck.