Horses actually evolved in the Western Hemisphere but became extinct here about 12,000 years ago - probably the result of that big "climate change" called the Ice Age. But they survived in Asia and elsewhere in the East. They were re-introduced to the Americas by your "invading European hordes."
This article confuses me though. I did some research on the fossil horse Eohippus shoshonensis gidley, sometimes called the American zebra. It was about the same size as a modern Arabian horse. In fact I knew the man who discovered it in the Hagerman (Idaho) fossil beds. Most sources say those fossils date back 3 1/2 million years. This article says the new discovery dates Equus back as much as 4 million years, "twice as long as they previously believed." Huh? It doesn't compute.
They must be talking about equus, the modern horse. Ancestors go back some 50 million years as you note. The modern horse isn’t found in rock older than the Pleistocene. At least it hasn’t been found in older rock, yet.