Some of the stallions use an interesting strategy; they face a rival, show off a bit of machismo, then fake like they are going to submit or back away slightly. This action causes the the other stallion to relax...then at that moment, the horse suddenly springs toward the unsuspecting rival and attack quickly.
In this image, the older pinto stallion is able to rear quickly and strike out with his hoof just as the other horse rises to meet him. The hoof strike just missed the browns head as he ducked away just in time.