Looks like she has some Arabian a couple of generations back. Hindquaters aren't strong, but her legs are straight (from what I can see) and she has a beautiful head. My guess is she'd be a pretty good hunter, on the flat and maybe even over some low jumps. Seems to have a wide heart space, so maybe with some training she'd be a fairly good competitive trail horse.
United States Hunter Jumper Association: www.ushja.org
North American Trail Ride Conference: www.natrc.org