My SSH loves jumping. She's just gotten old enough to start really working with her. We pop over odd cross rails a few times a month, but now we're starting gymnastics and grid work. She jumps just like any other greenie. Her legs don't fall off because she's gaited.
I've jumped from a pace before. The horses have a tough time setting themselves up to take off, so I wouldn't advise it. It's safe over small, well constructed fences; but it won't be pretty!
My mare jumps fabulously from a trot. I just put a few ground poles before a jump to get her trotting.