As an addendum to this topic ... instead of "fading away", perhaps the horse could just vanish after the same amount of time?
It's incredibly annoying to be maneuvering about in a free-wheeling cavalry battle and suddenly have your horse rear up in dismay from crashing into a mount that's barely visible ...
If they're going to stick around, at least let us see where they are so we can avoid them.
Or maybe they could just keep going off the edge of a map. I'm pretty sure that once its rider is dead, the horse will have enough sense to get away from all the screaming, dying, and sharp pointy metal bits.