Curly-haired horse?? Pinner said: A Curly is a breed of horse. Curlies, also called Bashkir Curlies, American Bashkir Curlies, and North American Curly Horses, come in all sizes, colors, and body types but all carry a gene for a unique curly coat of hair. The Curlies are known for their calm, intelligent and friendly personality. They show an easily trainable temperament. They are also known for having a tough constitution and great stamina.