The pilot reported that he intended to fly his airplane on a cross-country flight over high mountainous terrain. After takeoff, the pilot climbed to 9,500 feet mean sea level (msl) in order to fly over mountains. He subsequently descended to 8,500 feet msl, and then he attempted to climb back to 9,500 feet to clear additional mountains. This second climbing effort diminished his fuel reserve, so the pilot opted to divert to a 7,160-foot msl uncontrolled airport short of his destination. While flying over the airport to evaluate its runway's condition, he noted that the runway was covered with snow. The pilot opined that because of the airplane's low fuel state, it was prudent for him to land. The pilot made a soft field landing on the runway. During roll out, the airplane's wheels penetrated the snow-covered surface, the airplane nosed over, and both wings and the empennage broke.