Check out this blog: The Jumping Percheron
The percheron in that blog is used for eventing and is in AMAZING shape. With the right conditioning, a draft horse can have the same endurance as any other horse. They are required to have endurance for the work they were bred for. Our Belgians work all day in the hayfield all summer and in the woods logging in the winter. I also took my 17y/o Belgian gelding on a 15 mile trail ride and he did fantastic, didn't even work up a sweat and we trotted most of it.
For a trail horse, a Draft is an excellent choise because they usually have more mellow personalities and are more sure footed. As for the breed, it is personal preference. I'm a Belgian owner so I say Belgians. A Percheron owner will tell you Percherons... Etc. I wouldn't worry about breed and would just find a horse that fits you and your needs.