I read a good quote the other day, it went something like 'every horse, can do every movement, of every discipline'. I agree with this. You can train any horse, to do anything. A quarter horse could be taught to piaffe, a warm blood to do a western spin or sliding stop, a Thoroughbred to pull a cart, and a Clydesdale to jump. Can every horse, do every discipline well? No. A western horse no matter how well trained isn't going to move like a warm blood, the warm blood isn't going to spin and cut cattle like a quarter horse.
Dressage in its original and purest form, was just a way of training a horse, to be as responsive, as athletic, and moving with as much power and quality as it could. Also it was, and still should be,training a horse to move and progress, in its schooling, in a way that kept it sound and healthy throughout its life. I read a book recently about the director of the Spanish riding school, they had one stallion that could still perform a piaffe, and passage, and be ridden at the unheard of age of 35.
My point with all this, is that you can train your horse to do whatever you want, no matter its breed, confirmation etc. So many people have lovely, sweet, but maybe not so talented horses. They go and sell this horse, and get a new horse, that suits the discipline they want to do, but find they cant work with the horse. they would be better to keep the nice sweet horse they enjoyed riding.
Sure for showjumping, there may be a limit, to how high your horse can physically jump. But dressage, you can train you horse all they way to grand prix. It may not be gold medal wining. but with patience and persistence, and realising your horses weaknesses and talents, you can get there. Even if it is just to play around with at home or personal enjoyment. Usally the ones that get to the top are the ones that just keep going, no matter the road blocks.
i worked in a top dressage barn for a year, straight out of high school. I saw some fugly, fugly horses get to grand prix, just through correct training. This to me is a sign of a good horsemen, that you can improve any horse no matter how untalented it is. One horse in particular was terrible, it had a ewe neck, cow hocks, what looked like double jointed front legs, was as muscular as a barn rake and when it arrived went around the arena like it was completely inside out. But it got there in the end, now it competes nationally, with its very happy lady rider.you may never want to get that far, but you can always improve your horse through training and understanding.
Training a horse is hard, some times you go for months without progress, sometimes the dont understand, they give you the wrong answer, they physcially struggle, but if you stick with it they will get there in the end, no matter what your goal. The rider makes the horse, not the horse that makes the rider.