The flight instructor and student pilot were practicing landings to a full stop. During the 6th landing, the student pilot over controlled the airplane during the landing flare. The flight instructor attempted to correct the flight control inputs; however, he was unable to overcome the strength of the student pilot on the flight controls. The airplane struck a bank of snow on the left side of the runway and nosed over. The left wing and fuselage were substantially damaged. The flight instructor reported no pre-impact mechanical malfunctions or failures with the airplane that would have precluded normal operation.