The airline transport pilot was making a personal cross-country flight under Title 14, CFR Part 91. The pilot said when he arrived at the destination airport there was 3-4 inches of new snow, and that the overcast and low light condition made everything look gray. He said the visual approach slope indicator (VASI) lights were inoperative, and the appropriate notice to airman (NOTAM) was issued. He said he turned on the runway lights, identified what he thought was the runway surface, and lined up the runway edge lights on his left. After the airplane touched down he said he realized that he landed to the right of the runway surface, with the right side runway edge lights on his left. The pilot said the airplane settled into deep snow, and impacted a snowbank, collapsing the landing gear. In a written statement the pilot wrote that given the snow and light conditions, using the wide area augmentation system (WAAS) instrument flight rules (IFR) approach would have aligned the airplane with the runway surface. The pilot said there were no known mechanical problems with the airplane prior to the accident. The airplane sustained structural fuselage damage during the accident.