The certificated private-pilot reported in his written statement that they had departed his home airport for a local area flight in the conventional landing gear airplane. Upon returning, he obtained the current ATIS information reporting winds from 270 degrees at 8 knots, and the landing runway was 21. He contacted the tower and was cleared to land. Tower personnel notified the pilot that the runway was icy, with braking fair. He landed with full flaps with an airspeed of about 55 knots. The pilot stated that he had configured the airplane in a right slip, with the right wing low to compensate for the crosswind. The right wheel touched down first, then the left wheel, at that point the airplane started to turn right of centerline. He input left rudder and applied the brakes, but the airplane lost traction on the ice. He subsequently applied left aileron and the left wing stuck the ground. The airplane slid off the runway and came to rest on its nose in a snow bank. In the recommendation section of the report, the pilot recommended a wheel landing in icy conditions to maintain control authority of the tail surfaces. According to airport personnel, on the day of the accident, the temperature was below freezing with winds about 6 knots from the southwest. They also reported that the runway centerline was clear and dry. A NOTAM (Notice to Airmen) had been issued advising that braking was fair, with patches of ice. In an interview with a National Transportation Safety Board (NTSB) investigator, one person from airport operations reported that there were skid marks on the runway prior to where the airplane had run off the runway, and there was no ice on the runway where the accident occurred. The pilot and pilot-rated passenger commented to airport personnel that they thought the airplane had been caught by a crosswind gust, and that the pilot had ground looped the airplane. Also, additional airport personnel overheard the pilot and pilot-rated passenger discussing about how they might have avoided ground looping the airplane. The pilot reported that there were no mechanical failures or malfunctions with the airframe or engine prior to the accident. The airplane sustained structural damage to the left wing during the accident sequence. According to a Federal Aviation Administration (FAA) inspector, the runway conditions were reported to be clear and dry on the day of the accident. Examination of the runway surface revealed impact marks on the runway from the left wing, and marks from the airplane's left main tire. The marks were slightly off center and arced to the right toward the snow bank that the airplane came to rest.