A few ways to get rid of ennemy HA's:

- Arrow barrage: HA's will normally lose a missile duel. Just make sure you have enough archer units in your army when facing an ennemy that uses HA's and concentrate your fire to make a HA unit rout/retreat faster

- Chasing them off: You can catch up to HA's with light to medium cavalry. It's not that hard to ambush a HA unit with 2 cav units oo your own. If you're Byzantium, you should have access to steppe cavalry, these are ideal to take down or at least chase of HA units. They'll probably be tired afterwards but they don't need much fighting power in there role as light cavalry.

- The SHC-tric: I discovered this tactic during a Volga-Bulgarian campaign. I was relying heavily on steppe heavy cavalry and came in contact with both western as eastern armies. I've noticed that most units of HA going up against SHC will lose one way or the other. SHC are armoured and will outlast all most other HA units in a pure missile duel and if they do catch up the ennemies HA are really done for. I don't think this is the case in vanilla MTW (VI) but in the XL-mod they even have AP missiles making them a sure win even when facing more armoured HA's. Just let them duel with another HA unit and wait for the chance to charge and decimate anything they're facing.