I do not have a draft cross but my BOs daughter does and she bought him to use for shows. She did show jumping with him, I don't remember the exact height of the fences but I do know they were pretty high.
Here's my girls.
I show both of them. My clydesdale does english please and a little dressage. She knows how to jump little jumps but I don't bother much with it.
My gypsy jumps, does dressage, halter, english pleasure, learning xc, and tricks.
When I used to show dressage, I did up my Shire-TBX's mane (as you can see from the pics in her profile, she has lots of it) in either a running braid or a lattice. I came to prefer the lattice because it looked cooler and more importantly, it was easier so I was less likely to screw it up.