The commercial certificated pilot was landing on a snow-covered runway at the conclusion of a Title 14, CFR Part 91, cross-country positioning flight. The pilot reported that he had crosswind of about 15 knots, oriented about 30 degrees to the right of the runway heading. As the airplane was in the landing flare, the pilot said that a gust of wind pushed the airplane to the left. The right main landing gear tire touched down to the left of the runway centerline. The pilot attempted to correct the position of the airplane, and attempted to abort the landing, but the left elevator struck an unknown object, and the airplane pivoted to the left. The nose landing gear was torn off, and airplane came to rest along the left side of the runway.