The pilot stated that he did not verify the quantity of fuel in the airplane's fuel tanks prior to departure. About 15 minutes into the flight, the engine began to "sputter," then experienced a total loss of power. After looking at the airplane's fuel gauges, the pilot determined that the airplane had "run out of fuel." The pilot subsequently conducted a forced landing to a snow-covered field. Upon touchdown, the airplane nosed over and came to rest inverted, resulting in substantial damage to the right wing. The pilot reported there were no mechanical malfunctions or anomalies that would have precluded normal operation of the airframe or engine.