Most of the information I've read refer to the minis of old used in pit mines and the newer breeds such as the American mini. But most seem to agree they were breed from the smallest specimens available from different pony breeds.
http://www.theminiaturehorse.com/historyminiatures.htm
This link states the falabella (the smallest mini breed in the world) was developed from the Andalusian, which is a horse breed further supporting this theory.