Local folklore describes the Assateague horses as survivors of a shipwreck off the Virginia coast. While this dramatic tale of struggle and survival is popular, there are no records yet that confirm it. The most plausible explanation is that they are the descendants of horses that were brought to barrier islands like Assateague in the late 17th century by mainland owners to avoid fencing laws and taxation of livestock.
Assateague's Wild Horses - NPS

The Chincoteague Pony became an official registered breed in 1994. The average height of a Chincoteague Pony is between 12 and 13 hands (any horse that stands less than 14 hands is considered a Pony). Chincoteague Ponies are stocky, with short legs, thick manes, and large, round bellies. Chincoteague Ponies