Not a cross I would recommend... WP horses have a natural slowness, while reining horses have a natural "go"... But it's hard to say sight unseen. You might get a best of both worlds where you could do a little pleasure, reining, western riding, and pattern. Or you could get a horse with neither... Probably won't be the best of the best at either particular discipline.
But, hey, I'm the person who bred her WP mare to a HUS stallion because I wanted a versatile all-around/pattern horse. I got what I wanted.