Like smrods said, drafts aren't going to your first choice to excel in any riding discipline. Drafts are made to pull and be in a harness, so right there you start off with the disadvantage of not being built to be a riding horse. Their build influences their ability for self carriage, hind end engagement, and ability/ease to support a rider properly. Or rather lack there of.
That being said, a draft is a horse, and like any horse (baring unsoundness) you can train him to the 9's... or as far as his physiology lets him. In terms of events, the ones you will probably have a chance of doing better in are the ones more influences by finesse and training than the horses' natural movement. In english riding you might have more luck in things like low jumpers and equitation classes. In western, classes like trail, horsemanship, showmanship, and western riding require a lot of training an precision. They are judged more so on your ability to handle/control your horse, and how well your horse responds, and less on the horse's natural way of going. If I were you, those are the class types and skills I would focus on. You probably won't be in the ribbons in bigger shows (most big western shows are breed shows anyways), but there's no reason you can't be competitive at a smaller/local/fun level.