Moseley was born in San Juan, Puerto Rico. In 1978, he saw snow for the first time when his family went on a trip to California. Eventually, his family moved to Tiburon, California, a suburb north of San Francisco where he attended The Branson School in Ross, California. His family would go to the Sierra Nevada every weekend. This, and the fact that he was a better skier than his brothers, inspired the then nine-year-old Moseley to take skiing lessons. In 1992, he joined the Squaw Valley Freestyle Ski Team and soon won his first Junior National title in Freestyle Skiing; he graduated from high school in 1993 and that same year was selected for the U.S. Ski Team.