Quarter Horses are generally considered a 'working breed'. There more known for doing 'ranch things' like barrels, poles, cutting, sorting, roping, etc.
Thoroughbreds are lighter, sleeker horses bred mainly for racing, but also excel wonderfully in other disciplines. I've read stories of many off the track Thoroughbreds whom found successfully carriers in all sorts of things, mainly English riding.
I'm not to familiar with Warmbloods. I do know that there generally very expensive and are used extensively in English riding such as Dressage and jumping.
Wait! I'll fix it....