Drafts are the embodiment of what is meant by "cold-blooded" in horse terms. One of the reasons that the draft and draft crosses were preferred (beyond the simple ability to carry more) has to do with that stolid temperament. A cold blooded horse is more likely to deal with the chaotic conditions of war, take it in stride, and continue to do its job. Hot bloods are more reactive, and more likely to stress out, even to the point of nervous exhaustion.
I knew a stud that was 15/16ths Arabian, that was trained in dressage. He was supposed to have been really good at it, and to have been a fairly popular baby daddy in some part of New England. When the market for horses crashed a few years ago, he was put out of work; however talented his offspring may have been, they were always on the small side (he was barely 14 hh) and there is only so much call for mixed breeds. His owner surrendered him to a rescue, which in turn traced him back to his original breeder, who took him back when he was about 16 years old. Jazz was about as pleasant-natured a stallion as you'll ever meet; the breeder didn't know any dressage riders so we never got to see whether he was really as good as they say he was in the ring.