Horse crossbows are a terrible thing.
They're terrible because they're the rationalization of hit & run tactics. Hit an enemy from where he can't hit you, and keep doing that.
It's what all military doctrine tells you to do.
I am a pikeman. A plain and regular ole pikeman. I have a long melee range, but I'm not effective against anybody unless I'm helping someone else, or fighting melee cavalry.
The only way I can fight a horse archer or horse crossbowman is by taking cover in a place where I force him to fight me on equal terms, implying I'm not in some open field, in which case I'm absolutely fucked without a friendly ranged or shielder.
Sad but true. Mounted archers can pick who they fight, and when they fight, without any consequences that aren't avoidable by skill.