I don't compete but in my equestrian center I saw people using clay and standing wraps, but they also massage the back, the neck and a little bit the legs, the horses seem to really appreciate. I would like to learn those massage techniques!
I like to stretch my horse after a show, so he can unwind his back. I also do a quick trotting to take some fresh air :) For the cares, I apply clay on the legs and some standing wraps
I really keep a close watch on the horse's legs, to be sure he is not engorged. The day after a competition, I like to let the horse in the field, so his body can rest from the show. I also shower the legs (but not in winter) and apply clay.