The private certificated pilot/student, seated in the left seat, and the certified flight instructor, seated in the right seat, departed on a VFR instructional flight for the purpose of mountain flying instruction, and an Aero Club airplane checkout. The instructor decided to have the pilot land at an airport that had a 2,088 foot long runway. The first approach to the airport was high and fast, and the landing approach was aborted. On the second approach, the airplane was again high and fast (75 knots), and touched down about 600 to 800 feet beyond the runway threshold. The runway surface was compacted snow and ice, and the braking action was poor. The airplane collided with a snow berm at the end of the runway, and received structural damage to the landing gear and fuselage. The flight instructor did not take control of the airplane at any time before or during the accident sequence.