Predators don't start things they aren't sure they can finish. A "natural" encounter of this kind would be an ambush of the cougar landing on the horse's back and severing the spine/neck with a single bite: cougar wins. read more
If the cougar misses that first strike and gets below the horse - the horse is 1,000 lbs of very angry animal. A single kick or stomp and the cougar is dead: horse wins. There is no natural scenario of a "fair fight" between these species. Cougars don't get close to horses except to ambush them. Horses don't get close to cougars unless being ambushed. read more