Its behavior can threaten you because of its larger body mass. Even a newborn foal can outweigh many of the people it encounters. You deal with a large animal that can inflict injury, even if it doesn't mean to. Besides the horse's size, its behavior compounds the dangers. Few horses deliberately attack humans.
Horses tend to react suddenly and, to many people, unexpectedly.
That sudden motion can be dangerous if you're in close range. The horse bounds to the side in one jump, and steps on a bystander. A horse flings up its head, and the top of its neck hits the rider in the forehead. The impact knocks the rider off the horse. In an indoor arena, a horse bucks, and the rider's head collides with a wooden roof support.