During the landing roll the airplane impacted a snow bank situated alongside the runway and subsequently nosed over. The pilot reported that the runway was contaminated with snow and ice patches. The pilot stated that after touchdown the airplane "immediately began drifting toward the left side of the runway." The pilot reported that he attempted to correct for the drift using right rudder but "lost directional control" and departed off the left side of the runway. The pilot reported that he had 11 hours of flight experience in the airplane and the "runway conditions were much more than I was capable of handling with this aircraft." The accident airplane was equipped with a free-castering nose landing gear and directional control is maintained by differential braking when the rudder becomes ineffective at lower speeds.