Horses should simply, flat out, have less HP. THAT is the problem. The counter to cavalry was always ranged; but when a light horse can survive a crossbow bolt, or 4 arrows, then it is not a counter. Furthermore, if you run into a lone spearman, you have good chances to not be dehorsed instantly unless it is a str monster.
Bumping damage is fine. It was introduced to fix a totally broken mechanic.