Tinyliny, google Papa's Royal Delight - he's a registered TWH stallion here in Missouri who has mopped up in the 'natural' TWH classes. Here's a video of him cantering. This is achieved by breeding, training, and no soring practices or chains.
In fact, his owner is a gifted gaited horse trainer, horse lover, and tireless advocate of Friends of Sound Horses, which promotes sound shoeing and humane handling practices. I would love to have one of Papa's offspring, I think they move like magic.
It's a testament to the stoic, huge hearts of this breed that they 'try' to please these human beings who are truly torturers. Even the ones who don't 'make' - e.g., can't be trained as show horses because they don't tolerate the abuse -- are not winners even though they escape the torture.