The primitive horse species went extinct in the Americas at he end of the Pleistocene...11,000 years ago...at the same time as the Wooly Mammoths, Wooly Rhinos, Dire Wolves, Cave Bears, American Lions, Spotted Hyenas and the American Cheetah...numerous species...went extinct. The domestic horse now running free in the "Wild West" are feral, but the exact same species as an Arabian, a Morgan, a Shire or a Shetland. 
As for your assertion that the horses live in harmony with nature...that is not true in most HMA's. "Harmony with Nature" would mean that the horses have a predator that keeps the population in balance. (like the African lion keeps the zebra in balance) Only a couple of HMA's have any large predator that does that: a couple have Mountain lions that will kill foals, but most HMA's aren't Mountain lion habitat.
Scientific facts, as stated by the National Academy of Science, is pretty clear. People can read abut it here: