During an instructional flight, prior to landing, the pilots over flew the runway at pattern altitude to assess the runway conditions. The runway was observed snow-covered and appeared to have “recent tire track marks down the center of the runway”. The pilots chose to attempt a landing; however, during the touchdown, on the snow-covered runway, the main landing gear dug into the snow and the airplane decelerated rapidly. Subsequently, the nose-wheel entered the snow, “pivoting the airplane onto the nose”, and both wingtips struck the ground. The airplane sustained substantial damage to both wings and the empennage. The pilot reported no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The airport supplement remarks state: “Unattended. Be alert rwy condition not monitored. Recommend visual inspection prior to landing.” The flight instructor added that this accident could have been prevented by calling the airport and inquiring about the condition of the runway before the flight.