The student pilot reported that he was on a solo cross-country flight and the takeoff, climb, and en route portions of the flight were uneventful. He expected to perform a touch-and-go landing at the accident airport. During the approach, he noticed that the runway had patchy snow on it. Upon landing, the airplane veered to the left, which the student pilot believed was due to the unresponsiveness of the controls and the ice. He decided to change to a full stop landing and applied the brakes, but the airplane struck a snowbank on the left side of the runway, and it tipped forward and to the right. The airplane’s right wing was bent up at the tip resulting in substantial damage. The student pilot stated that there were no mechanical anomalies with the airplane that would have precluded normal operations. The airport manager confirmed that the runway had patchy compressed snow covering about 25% of the runway surface.