If you insist on a foot army, you'll probably need nothing but pantadapoi phalangitai against horse archers. I consider this an exploit, but here is the trick anyhow. Just recruit at least a half stack army of pantadapoi (in huge settings) and make a line long enough to prevent skirmishing escapes. Then you just continuously shrink your line as you walk towards a corner.
As soon as the horse archers touch you it's game over for them, and as you are slowly closing in on them in one solid line they have less and less room to maneuver. You won't take a lot of casualties from missile fire, and if any sort of heavy cavalry charges your (probably) thin line, you can halt all troops and have the two nearest units assist the charged unit. Their AP axes will take out the enemy heavy cav in no time.
This trick works wonders on horse archers and avoidance style fighting in general. Gotta love a any sort of map with borders.
Now if they had the ability to feign retreat for weeks at a time, like the Mongols in history, then this tactic wouldn't work at all.
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