Any horse in the fields or in the wild would get an accident while galloping or free running. Even a dog can break its neck if you let it run in the woods (as one episode of Supervet showed). These horses are very well taken care of and are even treated better than some humans (air conditioned stables, eating the best food they can have, best vets to look after them, etc.)! Horses won't run or jump if they don't like to. Many races have shown this (we watch horse racing every single day on TV).