The instructor pilot of the tailwheel-equipped airplane reported that he was conducting a tailwheel endorsement training flight for another instructor pilot who was seated in the right seat as the pilot flying. After the pilot under instruction conducted multiple touch-and-go landings on the maintained asphalt runway, the instructor pilot decided to have the pilot conduct a touch-and-go on a snow-covered runway that was used by ski-equipped airplanes in the winter. The pilot landed in the center of the runway where the snow had been packed down by skis; however, the airplane drifted right after touchdown and the pilot attempted to correct back to the middle with the instructor pilot’s assistance. The right main landing gear tire “caught unpacked snow” which caused the airplane to turn rapidly right and flip over onto its back. The vertical stabilizer and right wing lift strut sustained substantial damage. The Federal Aviation Administration’s master airport information states that the runway is used seasonally as a snow runway (ski-equipped aircraft use recommended to minimize wheel rutting.) The instructor pilot was very familiar with the airport, where his flight training school was located. He likely knew that the runway was normally used for ski-equipped airplanes, and that unpacked snow or wheel ruts from other airplanes were potential hazards during the instructional flight. The instructor pilot stated that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.