THE PILOT REPORTED THE ENGINE LOST RPM, SPUTTERED AND STOPPED ABOUT 10-12 SECONDS AFTER TAKEOFF. THE AIRPLANE STRUCK SOME TREES DURING THE FORCED LANDING. FAA INSPECTORS WHO EXAMINED THE AIRPLANE COULD FIND NO ENGINE ANOMALY WHICH WOULD CAUSE A LOSS OF POWER. THE TEMPERATURE WAS 51 DEGREES, AND THE DEW POINT WAS 43 DEGREES. THESE TEMPERATURE/DEW POINT CONDITIONS ARE FAVORABLE FOR SERIOUS CARBURETOR ICING. THE PILOT STATED HE DID A CARBURETOR HEAT CHECK ON RUN-UP. THE FAA INSPECTOR WHO EXAMINED THE WRECKAGE REPORTED THE CARBURETOR HEAT WAS IN THE 'OFF' POSITION.