Since horse archers made up only a part of their army I would concentrate on his infantry first and leave the annoying mopping up for later. You don't have to get the HA's just keep their harrassing to a minimum. I would put spears in front, Inf behind, with archers and cav to the wings. Advance obliquely and try not to give their archers any height advantages. As you advance, if they shoot from the flanks sent your archers after them with cav in support. If they mass in front, break up their formation with a quick cav charge. Again you don't have to catch them only disrupt their fire as you close on their main line. They will regroup and follow your retreating cav so you lead them back to your archers. Ouch

If you can break their main line then you should be able to catch or drive off the HA's. The trick is to march your infantry into the space where your cav is driving them and grind up as many as you can.

It will take awhile but eventually they'll say screw it and retreat. Of course you'll have to keep their reinforcements in mind but the AI usaully goes into attack mode with them and you can have them break against your reformed spears.