No, I don't think it's their "natural" temperament.
I do know a few horses that have had not-so-great riders who pretty much just taught them to go-go-go on trail all the time. The end result is a horse that isn't "hot" but very nervous and with no real concept of moving at a relaxed, comfortable flat walk.
My boyfriend's sorrel TWH gelding was heading in that direction, thanks to a previous owner who was always pushing to go faster, and always in the front of the group. If the horse so much as stumbled, the old owner jerked the horse in the mouth and bumped his sides. By the time my boyfriend bought him, the gelding would have these meltdown-moments where he'd completely freeze, and he would work himself into a lather before he was even on the trail.
My boyfriend only rode the gelding as a "back up" when he went on riding/camping trips, to give his primary horse a break. He just didn't enjoy riding that horse because, as he put it, "it always turned into a battle." By some people's definitions, I guess he could have been considered "hot," but it was more of a learned-behavior issue than a temperament one.
Last summer, I ended up taking the horse for a couple of months (because I wanted a project) and put a lot of miles on him, mostly solo. As it turns out, there really isn't a mean or rank bone in his body. . .has a really
good mind when he uses it. . .and he's a heck of a great trail horse
once he learns how to relax.
The gelding has since become "my" horse for our camping trips.