Horses may well be extinct in the Fallout Universe. They were pictured in the All Roads comic but Chris Avellone said- "there were parts of the New Vegas design where we specifically removed the mention of horses from certain narrative points (one of Raul’s stories originally referenced horses, for example, and we cut them because we didn’t want to imply horses still existed)." You could possess the last horse in America or something I guess, or they could be engineered GECK style.
Not sure how I feel about horses in FO, I think I'd rather keep them in the Elder Scrolls games and have at most rare quads/buggies. With the new mad max coming out Bethesda might try to capitalise on it.