It would ofcourse call for a new set of animations be completed for riders being knocked down, but I can picture a few circumstances where it does not get to look like a mess, as long as the game at some point "Fixes" the huge delays there is when I am waiting for people to stand up again from prone.
It would for example not look ridiculous if the rider was knocked off the horse (and not be ridiculous in terms of physics either) and then spent a turn hopping back up on the horse.
The horses are not intelligent enough or viable combat members enough to have theyre own turns (IMO) while it might be a possibility, it would make combat silly if 1 unit splits into 2.

Another reason would just make the prone animation into a "Stunned" animation, the rider needs to regain balance on the current mount.

Sincerely
~ Kongdej