Just spec an horse archer and continously harrass other horse archers. Go full anti low armour build with Tatar Arrows and aim for the horse only if they use weaker ones. This will greatly diminish their effectiveness and piss them off. They are forced to shoot you first or get their horse killed, so in any case you diminish their ability to shoot your team and if you kill their horse, they are fucked. If you have little faith in your ability to win horse archer duels, then just stay at range as much as you can, but never stop harassing the cunts. Force him to pay constant attention to you.
I played some today and there were 25 players on EU 1 of which 3 were horse archers. After about 6 rounds of me doing this, they had left. You should only shoot horse ranged until they are dead, and then just bumpslash the enemy. You want to reduce the strain on the server of horse ranged, so if you go ahead and be horse ranged yourself, then you become the problem. If I play and horse archers come on, I am just gonna do this, it is quite satisfying to see their effectivity drop and watch them leave.