pretty sure harness is for having the horse pull a small cart, look up harness racing (they usually go a mile in about 2minutes). maybe give horses stats like agility and strength? so horses can be work animals and pull small carts/wagons/ploughs or bread for horseback riding.
horses also have different gates (foot placement when walking), trotting and pacing, before a gallop. if that helps any
horseback riding also has a lot to do with the rider, if the rider knows what he is doing then the horse will last longer. when a horse gallops it is airborne a little and if the rider knows how to ride he will sort of bounce/move with the horse, almost standing while riding, to reduce the weight strain.
can we have size be a factor? smaller requires less food but all quantities are less

then we can have minis and maybe donkeys haha