Ok, I should break the situation into two, one is charging and one is hand2hand.

For Charging Situation, I agree that calvary unit have advantage to overkill. What you could do to them is spear them while they're charging or batt your sword on horse's head like an incoming baseball. Hope this would freak the horse out and make them panic and jump around uncontrolably.

For Hand2hand Rumble Situation; once the horse slow down into h2h, they will become a passive target that just stood there waiting to be stabbed by infantry on the side or behind its ass. Also, they can't be controlled as wish so the rider will be facing toward whatever direction the horse is facing. They can't turn left/right or 360 degree so quickly while infantry can. So, infantry have much open opportunity to take down the horse.

This is where I think horse isn't very useful except for traveling.

Well, i don't really have the imagination of the real battle. Maybe after watching braveheart I'll post back again.

As for elephant, can a sword/arrow/spear go through its skin? Why the 5th post says only the weakpoint is the head?