The private pilot topped off both fuel tanks (40 gallons each) prior to departing on a cross country flight in his single-engine airplane. The pilot stated that he had difficulty securing the fuel cap on the right wing tank after refueling. About 2-hours into the flight, with the fuel selector on the left tank, the engine stopped producing power. The pilot noted that the left fuel guage read empty and he attempted to switch tanks. He was unable to re-start the engine and made a forced landing to a deeply snow-covered field. The airplane sustained substantial damage to the wings, firewall, and fuselage. In addition, both wing fuel tanks were found empty and the fuel cap on the right wing was missing.