What happened
During the cruise phase of flight, the engine began running roughly and subsequently lost power. The flight instructor followed emergency procedures, which initially allowed the engine to regain power. In an attempt to troubleshoot the failure and allow more time for troubleshooting, the throttle was reduced to 2000 RPM. However, once the throttle was reduced, the engine quit a second time.
The flight instructor applied carburetor heat, but the student pilot subsequently removed the carb heat. This cycle of applying and removing carb heat occurred several times, resulting in intermittent losses and gains of engine power. Eventually, the engine could not regain power, necessitating a forced landing. The aircraft landed in a frozen swamp area that was covered by 2 1/2 feet of snow. During the landing, the aircraft nosed over.
The occupants were not injured.