The student pilot reported that he took off from Runway 34 and intended to practice take-offs and landings. After landing the airplane without incident, he raised the flaps and added full power to take off again; however, the airplane veered to the left during the take-off roll. The student pilot added right rudder to keep the airplane on centerline but was unsuccessful. Once airborne, the left wing struck a snowbank on the side of the runway, which caused the airplane to pivot left. The nose gear collapsed, and the airplane came to rest inverted, nose first in the snowbank. The outboard side of the right wing sustained substantial damage to the skin, ribs, and spars. The student pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. At the time of the accident, Runway 34 was covered in ice and snow.