It isn't the breed of horse that matters, what is important is conformation. The horse can have all the heart in the world, and all the want to do the sport in question, but can the horse physically handle it.
As Kacha said:
However, the most important things will be conformation and temperament
Conformation is very important, if the horse is not built to do it, the horse will physically break down.
I have seen many TB's do well, and I have also seen many TB's not make it. I have seen QH's, Appy's, Pony's, Mixed Breeds merge into Mid and Upper Levels, and I've seen many not. Same with WB's and Sport Horses - it isn't the breed that matters, it is the conformation/build of the specific horse.
Of course, spirit/want/heart is important as well, you can have a horse with wonderful conformation, but no heart - that doesn't do you a lot of good either. Still, conformation is very important.