The student arrived at the airport on a cross-country flight and requested landing advisories on the UNICOM frequency. The student stated that somebody replied that runway 18 was in use. Before landing, the pilot overflew the airport 4 times. Two of these were low passes. The pilot noted tire tracks which he estimated were about one inch deep. However, the runway was covered with 8 to 10 inches of snow. The pilot made a soft field landing. During the landing roll, the aircraft slowly nosed over after it had decelerated and was almost stopped. The latest snowfall had occurred about 5 days before the accident. The runway had not been plowed after the snowfall nor had the nearest flight service station been informed of the runway condition. No airport personnel had made transmissions on the UNICOM just prior to the accident. However, there were several airports in the area that had north-south runways and utilized the same UNICOM frequency.