The pilot attempted a takeoff on a 50 foot wide runway that was snow covered, and plowed to a width of 15 to 18 feet. As he initiated the takeoff, the left main landing gear wheel entered the snow on the left side of the runway, which was about 16 to 18 inches deep. The pilot added more power and rudder; however, the airplane turned further into the snow and came to rest on its nose and left wing. The width of the main landing gear on the airplane was 7 feet, 8 inches.