On January 5, 1999, at 1630 eastern standard time, a Cessna 172P, N53637, sustained substantial damage on impact with a snowbank while landing on runway 27 (5,013' X 50' dry/asphalt), near Lambertville, Michigan. The pilots told authorities that on rollout the airplane drifted to the right and impacted a snowbank along the right side of the runway. The pilots reported no injuries. The 14 CFR Part 91 instructional flight was operating in visual meteorological conditions. No flight plan was on file. The local flight departed about 1530. In the pilot-in-command's written statement, the pilot indicated that the dual student was in control of the aircraft during the landing approach, flare and touchdown. The flight instructor stated that, "Upon touching down at normal speed on the ice-patched 50 foot wide runway, the aircraft drifted right of centerline with a contribution from a left crosswind." The flight instructor stated that he was unable to correct for the drift through the use of aileron, rudder, and brakes, and the aircraft subsequently slid into a three foot high snowbank along the edge of the runway. A post accident investigation was performed by the Federal Aviation Administration A functional test of the brake system revealed no anomalies.