Over-use of the whip in horse racing isn't allowed, Sammc. If injuries were found, there'd be an immediate inquiry.
I also agree with what the others've said about horse trials. Having been to Badminton recently, I can assure you that you can't make the animal do something which it doesn't want to. Many pull up, or unseat their riders - and this might have nothing to do with not wanting to jump or to do the course, because in the main, these animals are bred and trained for what they do, and enjoy the exercise.