N178AF

The instructor and his pilot-rated student were conducting instrument work; reported weather included a vertical visibility of 200 feet and 1/4 mile visibility in fog. After the first instrument landing system approach with the student at the controls, the runway was not visually acquired at the decision height and a missed approach was performed. The instructor took the controls for the second approach and asked the student to monitor the radios and look for the runway environment. At 400 feet above ground level, the instructor saw the runway below him, but the airplane was "slightly high on the glideslope and a little fast..." He elected to attempt a landing, reducing the throttle to idle and adding full flaps. The airplane touched down long and the instructor was unable to stop the airplane on the remaining runway. The airplane collided with a snow bank, resulting in structural damage to the fuselage.