O. C. Marsh argues that horses existed in the New World before the arrival of the Spanish.
O. C. Marsh, “Fossil Horses in America,” American Naturalist 8, No. 5 (May 1874): 288-294
It is a well known fact that the Spanish discoverers of America found no horses on this continent, and that the modern horse (Equus caballus Linn.) was subsequently introduced from the old world. It is, however, not so generally known that these animals had formerly been abundant here, and that long before,in Tertiary time, near relatives of the horse, and probably his ancestors, existed in the far west in countless numbers,and in a marvellous variety of forms. The remains of equine mammals, now known from the Tertiary and Quaternarydeposits of this country,already represent more than double the number of genera and species hitherto found in the strata of the eastern hemisphere,and hence afford most important aid in tracing out the genealogy of the horses still existing.