No one knows for sure. Research is continuing in that area.
Several theories exist.
Some people think that they came over the land bridge that linked Russia to Alaska centuries ago. The Curly horse in America was given the name of American Bashkir Curly by the founders of the American Bashkir Curly Registry in the belief that the horses were decended from the horses in the Bashkirky region of Russia who were thought to have curly hair. 161 A.D. Horses with curly hair have also been found in South America. Curlies have been a part of the history of the Native American peoples for over 100 years. The ancient legend among the Sioux and Crow tribes state that the curlies first appeared to the people as large, red, curly dogs.