“On Christopher Columbus’s second voyage to the New World he brought with him to the Caribbean Island of Hispaniola (which today forms the countries of Haiti and the Dominican Republic) 24 stallions and 10 mares, arriving on January 2, 1494.” (p. 11 of The World According to Horses by Stephen Budiansky, (c) 2000 by Stephen Budiansky, publisher Henry Holt and Company, ISBN 0-8050-6054-5.)
John Kessell writes, in his Spain in the Southwest (Copyright © 2003 by John L. Kessell, Published by University of Oklahoma Press, ISBN10: 0806134844, ISBN13: 9780806134840), that the horses were Andalusian barbs (at least, that is how I interpret this excerpt from his Chapter 1):
The domesticated animals they brought, especially spirited Andalusian barb horses and snarling greyhound and mastiff attack dogs, astonished the Tainos. Cows, pigs, goats, and chickens also came ashore and multiplied. When allowed access, Natives took readily to this tamed and assorted meat supply, as they did to material items like candles or scissors that proved more efficient than their own.
Image of Andalusian/Iberian from Wikipedia, which attributes this sketch as: “Welbeck Le Superbe Cheval de Spanie,” engraving (reprinted 1743) by C. Caukercken, after Abraham van Diepenbeeck, from the first Duke of Newcastle’s A general system of horsemanship in all its branches (new edition printed for J. Brindley, bookseller to His Royal Highness the Prince of Wales, in New Bond-street, 1743)
And in the Internet exhibition “No Traveller Remains Untouched” of The Albert B. Alkek Library of Texas State University, San Marcos, TX, they write of the reintroduction of the horse to the Americas:
The horse came to the New World – to Hispaniola – on Christopher Columbus’ second transatlantic voyage, on January 2, 1494. Hernan Cortes brought the first horses to New Spain (current-day Mexico) in 1519.
Update (11:25 AM): Wikipedia claims:
In 1518 Velázquez put him in command of an expedition to explore and secure the interior of Mexico for colonization. At the last minute, due to the old gripe between Velázquez and Cortés, he changed his mind and revoked his charter. Cortés ignored the orders and went ahead anyway, in February 1519, in an act of open mutiny. Accompanied by about 11 ships, 500 men, 13 horses and a small number of cannons, he landed in the Yucatan Peninsula in Mayan territory.
Image of Barbs from Wikipedia.
In Wikipedia’s article on the Andalusian horse, they say:
Mitochondrial DNA studies of the modern Andalusian horse of the Iberian peninsula and Barb horse [see also Preserving the Rare Beauty of the Abaco Barb on InfoHorse.com] of North Africa, present convincing evidence that both breeds crossed the Strait of Gibraltar and were used for breeding with each other, influencing one another’s bloodlines. Some of the earliest written pedigrees in recorded European history were kept by Carthusian monks, beginning in the 13th century. The Carthusians bred powerful, weight-bearing horses in Andalusia for the Crown of Castile, using the finest Spanish Jennets as foundation bloodstock. Because they could read and write, and were thus able to maintain careful records, monastics were given the responsibility for horse breeding by certain members of the nobility, particularly in Spain. Andalusian stud farms for breeding were formed in the late 1400s in Carthusian monasteries in Jerez, Seville and Cazalla. By the 15th century, the Andalusian had become a distinct breed, and was being used to influence the development of other breeds. They were also noted for their use as cavalry horses.
Update (11:30 AM): For information on the evolution of horses, see the page “Horse Evolution Over 55 Millions Years” of Tuft University‘s Department of Chemistry; Wikipedia’s article “The Evolution of the Horse;” Darwiniana.org‘s “Horses, Evolution, and Transitional Forms;” etc.