The pilot, who was chasing coyotes at low level over open snow-covered terrain, noticed that the airplane's engine was beginning to lose power and run rough, and that the airplane was starting to lose altitude. He therefore applied carburetor heat and full power, but just as the engine started to regain power, the airplane's main wheels broke through the crusty top layer of the snow. The airplane then began to slow, and when its propeller contacted the snow, the pilot pulled the power back and attempted to transition to a landing. Although the pilot had the control stick all the way back, the airplane nosed over onto its back, resulting in damage to the vertical stabilizer and the bending of both left wing lift struts. According to the pilot, except for the accumulation of carburetor ice, there were no problems with the engine.