Horses do not breathe by expanding and contracting their chest during canter and gallop. They expand and contract the chest when breathing at rest, when breathing at walk and trot, and perhaps most noticeably when blowing hard after exercise. But during canter and gallop, the air moves in and out along the lines of a syringe with the stiff wall of the syringe representing the chest and the plunger the diaphragm i.e. all air movement during canter gallop comes from movement of the diaphragm.