Ouray Meyers was born in Taos, New Mexico. His father, Ralph Meyers, was an artist, a writer, an Indian trader and the founder of the first trading post in Taos. Ralph was one of the central figures in New Mexico in the halcyon days before the rest of the world discovered it. Ouray's mother Rowena Meyers Martinez, a devotee of local, regional and state history, collected historical clothing and sponsored a historic fashion show. After Ralph's death, Rowena remarried. Her husband Paul Martinez, a Forest Service employee, taught Ouray and the rest of the family about his native Spanish culture. Growing up in this environment helped the artist gain an appreciation for the culture of Taos. His toys included an authentic Bowie knife that pioneer Jim Bowie used at the Alamo. The knife now rests behind glass in a Texas museum.
His formative years included association with many of Taos' leading artists of the day, all friends of the family. Frequent visitors to the home, the following people provided Ouray with their artistic influence: Walter Ufer; Joseph Sharp; Buck Dunton; Leon Gaspard; Nicolai Fechin; Dorothy Brett; Georgia O'Keeffe; Mabel Dodge Lujan; Giselle Loeffler; and Frank Waters. Some of the people listed above belonged to the Taos Society of Artists, the originators of the Taos Art Colony. Because of Ralph's close, trusted friendship with the Taos Pueblo people, Ouray received the birth name "Toshanee" or "Dawn Boy" from Taos Pueblo friends. Ralph Meyers' friendship with Frank Waters inspired the character of the trader in the book The Man Who Killed the Deer.