I bought a horse from someone and am making payments and we have no contract what happens if I stop?

You have no contract, but you shouldn't con this person because you just want to. One day you may come across this person again. He could sue you saying that you actually stole the horse (Long shot, but could happen) Be truthful in the horse world, because karma will bite you in the butt. If word gets out you might not be able to purchase a horse in the area you bought your current one or anywhere else close to you. Word spreads fast. Hope this helps.