It's just a matter of logic that HA are structurally unbalanced. Lets compare them with other classes to see which are their counters.
- Melee footman ? Obviously no. The only hope for shielders is not being bumpshot. 2h will automatically die.
- Melee cav ? No better. 3 Arrows in the horse, less with headshots. Then you are a gimped footman so you last even shorter.
So that makes HA simply immune to melee classes. I hope they have some serious ranged counters to balance that. Let's see.
- Archers ? Shoot, bump, shoot in any order = foot archer dead.
- Crossbowmen ? One bolt, even hitting, isn't going to do the trick.
- Throwers ? Considering it takes 3 throwing axes to kill an arab horse, that's not so great.
So the counters to HA are very poor indeed. At best they have 1/2 chances against the HA (archers). Now you might say that considering 1 vs 1 is not a good thing. Okay. Let's say 2 HA against any combination of 2 melee footmen and melee cav. Not better. The same for one archer defended by one pikeman (which is probably the best combo against HA) against 2 HA. One HA just shoots from the front and the other from the back and the job's done in no time.
So, my question is, how to kill horse archers without relying on the supposed mistakes they will make ? A class that is completly immune to more than the half of the playerbase should have some serious downsides too, but it's not the case.