At 1540 Pacific time, a Cessna 172S was damaged during a hard landing at Everett/Snohomish County Airport. Neither pilot was injured. The flight was an IFR instructional flight and an IFR flight plan had been filed. The flight had just executed a missed approach at PAE and when climbing through 1,000 feet the aircraft began picking up ice. The aircraft was cleared for the ILS Runway 16R approach and the pilot reported difficulty maintaining altitude. At about 10-15 feet above the ground, the aircrafts left wing dropped. There were a number of pilot reports of moderate clear and rime icing by aircraft overflying PAE at the time.