In Roy Andersen’s The Medicine Pony, a Crow warrior stands in front of his white pony, holding a horse dance stick after a late afternoon rain. The man gazes toward the horizon while two other Indians wait behind him on their mounts. Painted on the white pony’s neck are symbols of dragonflies, which to the Crow people were messengers from the spirit world that carried dreams to individual warriors. “I was pretty proud of the piece,” Andersen, 82, says from his studio in Kerrville, Texas. “Some of them you struggle through, and sometimes they just paint themselves. Those are the ones that are really fun. This one went along the way I wanted.”

Authenticity is a hallmark of Andersen’s work. “I always like to try to get a little w...