This article from 2002 posits that horses were domesticated in multiple locations, at different times, by different people, so that unlike domestic cats (which all trace back to a Middle Eastern ancestor), the modern horses of the world tend to trace back to various regional ancestors. As has been suspected the Andalusian, Lusitano and Barb are closely related. The Arab is not related to this group (as one might guess by the appearance). About 30% of North American Mustangs, as well as many South American breeds, trace back to the Andalusian/Lusitano/Barb (as might be expected from the Spanish colonization of the Americas). The northern ponies such as Shetland, Fjord and Icelandic are closely related, and similar to horses found in Viking burial sites in Scandanavia.
I'll post more on these matters in the future, as horse breeders tend to be quite interested in issues of antiquity and purity in their favorite breed.