5,000 years ago: horses were first domesticated
There are many horse paintings in European prehistoric caves from 30,000 years ago, but these were not domestic animals, they were wild ones and most probably hunted for meat.
The results of DNA analysis performed on domestic horses show that all present breeds evolved around 5000 years ago in the region of Dereivka, Ukraine, near the Black Sea. Starting with these specimens, humans artificially selected for tameness the most docile horses and used them afterwards as working animals.
The evolution of horses, starting in America 50 million years ago from the dwarf, dog sized, forest dwelling Eohippus, through a series of transitional fossils, to the present breeds, is well understood.
We also know there were horses in America until about 15,000 years ago when humans migrated from Asia through the Sea of Bering and brought them to extinction, probably due to excessive hunting.
When Europeans arrived in America in the 15th century, bringing with them their horses, the inhabitants of the New World were unaware of these animals since their ancestors had been responsible for their extinction across the whole continent.