I wish I could find it, but I had an article in one of my "Voice" magazines about a TWH that jumped. Might be on the TWHBEA website? Anyways, not real common, but definitely a possibility. LoL, if I were a decent rider I would get my girl into it, because she LOVES to jump 4 foot fences.
Yeah, they canter...it's just more of a rolling canter. It's actually called a "rocking horse canter" for obvious reasons.
Supposedly smoother...lol, I dunno about that. My horse is only 3 so I've only cantered on her once, and that was by accident.