Two Akhal-teke stallions were among the three founding studs of the Thoroughbred breed. The Stavropol Stud in Russia breeds Akhal-teke horses, the famous Golden Argamacks of ancient lore.
The following pictures of Gench, a highly valued sire of Akhal-tekes, strongly resembles early Thoroughbred race horses like the one in that painting. Take a look:
http://www.stavropol-teke.ru/en/gallery/Gench/