The pilot reported that while in level cruise flight, the engine began to run rough and lose power. Unable to restore full engine power, he selected an area of snow-covered terrain as a forced landing site. During the forced landing, as the main wheels contacted deep snow, the airplane nosed over, sustaining substantial damage to the right wing lift strut. The pilot noted in his written report to the NTSB that carburetor heat was applied after the initial loss of engine power, and that he was only able to maintain 1,100 engine rpm before the forced landing. At time of the accident a weather observation station located about 25 miles northwest of the accident site was reporting, in part: temperature, 45 degrees F; dew point, 41 degrees F. When the temperature and dew point are entered into a carburetor icing probability chart, the result is in the "Icing-cruise or climb power" category. A Federal Aviation Administration (FAA) airworthiness inspector from the Anchorage Flight Standards District Office traveled to the pilot's private airstrip, and examined the airplane after it was recovered. The inspector reported that he was unable to find any preaccident mechanical problems with the airplane. During a subsequent follow-up conversation, the pilot reported that there were no preaccident mechanical anomalies with the airplane, and given the temperature and dew point at the time of the accident, the loss of engine power was likely due to carburetor icing.