According to the pilot, his intent was to perform a touch and go landing on a runway with patches of snow extending from the approach end to the departure end. The pilot reported that the touchdown and landing roll were uneventful. He reported that as he aborted the landing and configured the airplane for takeoff, he retracted the flaps, advanced the throttle and applied right rudder. He recalled that when he advanced the throttle, the airplane immediately made a sharp left turn, exited the runway to the left, and impacted the residual snow that was previously cleared from the runway. The airplane nosed over and the pilot exited the runway under his own power. The airplane sustained substantial damage to the vertical stabilizer and both wings. The pilot reported that there were no mechanical failures or anomalies prior to or during the flight that would have prevented normal flight operation.