According to the pilot, the landing on the ice runway was smooth, but the airplane began to drift left. The pilot was hesitant to use heavy rudder and brake inputs, as he was unsure of their effect when landing on ice. As the pilot continued to apply right rudder, the left main landing gear began “dragging on snow”, which prevented the plane from turning right. The airplane veered into a snow bank resulting in substantial damage to the firewall. The pilot reported that there were no mechanical malfunctions or failures of the airplane. A crosswind at 16 knots, gusting to 23 knots, was present at the time of the accident.