The rich fossil record of equids has made them a model for evolutionary processes. Here we present a 1.12-times coverage draft genome from a horse bone recovered from permafrost dated to approximately 560-780 thousand years before present (kyr bp). Our data represent the oldest full genome sequence determined so far by almost an order of magnitude. For comparison, we sequenced the genome of a Late Pleistocene horse (43 kyr bp), and modern genomes of five domestic horse breeds (Equus ferus caballus), a Przewalski's horse (E. f. przewalskii) and a donkey (E. asinus). Our analyses suggest that the Equus lineage giving rise to all contemporary horses, zebras and donkeys originated 4.0-4.5 million years before present (Myr bp), twice the conventionally accepted time to the most recent common ancestor of the genus Equus. We also find that horse population size fluctuated multiple times over the past 2 Myr, particularly during periods of severe climatic changes. We estimate that the Przewalski's and domestic horse populations diverged 38-72 kyr bp, and find no evidence of recent admixture between the domestic horse breeds and the Przewalski's horse investigated. This supports the contention that Przewalski's horses represent the last surviving wild horse population. We find similar levels of genetic variation among Przewalski's and domestic populations, indicating that the former are genetically viable and worthy of conservation efforts. We also find evidence for continuous selection on the immune system and olfaction throughout horse evolution. Finally, we identify 29 genomic regions among horse breeds that deviate from neutrality and show low levels of genetic variation compared to the Przewalski's horse. Such regions could correspond to loci selected early during domestication.