The pilot reported that on a previous flight the airplane had been filled and flown for about 3.8 hours, he attempted to refuel the airplane but the self-service fuel station at the departure airport "failed to dispense fuel". The tanks were "checked visually" and after calculations, he determined that there would be enough fuel to make the flight. After departing, during cruise flight, about 1,800 ft above ground level, the "engine stopped." He set the "best glide speed" toward a nearby airport. As he approached the airport, it "became apparent that they would not make the airport." He then executed a 180º turn and landed on a snow covered, frozen lake with the landing gear retracted.

The airplane sustained substantial damage to the left wing and fuselage.

The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.