Horses and ponies often grow horny protuberances on their legs known as chestnuts and ergots. Chestnuts are usually found on the inside forearms and sometimes on the inside hinds of horses, while ergots are the hard knots at the point of the fetlocks.
In most horses, these horny growths shed naturally over time. However, if you want to keep your horse's legs looking smooth, you can help the process along by applying petroleum jelly. This softens the tissues and makes the layers easy to peel away to surface level. Soaking with warm water and a mild soap during bath time has the same effect.
If chestnuts and ergots have already grown long, hard and unsightly, you may want to clip them off with a pair of nippers. Like your fingernails, they have no blood supply above the surface layer of the skin, so nipping them off won't hurt. It also does no harm to leave them intact. If chestnuts and ergots are showing exuberant growth, though, it could be a sign of a health problem, such as laminitis.
Interestingly, not all equines grow ergots, and many horses and donkeys have only the smallest of chestnuts on their forelegs and none on their hinds.