Decreasing skills - at least to zero - doesn't break anything. Works fine; just feed troop_raise_skill a negative number. Post-combat, you could also take away from the troop his "healthy" centaur lower half item and substitute a "crippled" one instead - easy. But surely the aftereffects (crippled or whatever) are the least of your worries?
If you check the health of the horse frequently during combat, you could make damage to the horse (as percentage or absolute, your choice) reduce player health as well. Can't kill with that, it just reduces HP, doesn't "damage" agents - you'll have a situation where the killing blow must be to the upper part, but even a zero-damage hit will probably be fatal if you've been triggered down to zero HP. If you do it as a percentage thing and set it up right, you can even guarantee that by the time the horse dies (potentially breaking the combo), the rider's also under sudden-death at least. Or you could record the damage, damage the player, and then heal the horse, so it only ever dies if it dies within one shot (or several so close together the code doesn't notice); odds are the upper half will always go first under those conditions.
In the Python scheme exchange thread I posted the code I use to figure out which agent # is the horse corresponding to a particular rider. You'd want that. Probably also want a code to shut the whole thing down if he dismounts for some reason; the code I've got will at least detect if he dismounts, after that it's up to you (freeze him in place with invisible scene props and/or programmed movement, drop him to zero HP, spawn a black curtain or cloud of flies to hide it from vision, whatever you can think of - can't outright remove him, though.) If the rider's Athletics is very poor and his Riding very good, the AI will probably resist dismounting as much as it can; still wouldn't want to combine that with my urban alleyway-ambush scene, though.
You'll also need a way to keep remaining lower-halves from wandering the field riderless. Can spawn barriers around them as a 'fence' so they at least sit still, while keeping the walls low enough that they can still get shot/chopped, and will die soon enough (since when you detected the rider dead, you of course put the horse into sudden-death-state as well).
Basically, it's doable, but it's a hell of a chunk of code when all's said and done - and that's ignoring the rigging issues entirely.