THE PILOT REPORTED THAT HE NOTICED A BURNING SMELL, SHORTLY BEFORE HE LOST COMPLETE ENGINE POWER. THE PILOT SELECTED A NEARBY FIELD, AND ATTEMPTED AN EMERGENCY LANDING. WHILE MANEUVERING FOR THE LANDING, THE AIRCRAFT COLLIDED WITH TREES. AN EXAMINATION OF THE ENGINE REVEALED A HOLE IN THE EXHAUST MANIFOLD CAUSED BY CORROSION. THERE WERE INDICATIONS OF FIRE ON THE AIRCRAFT AIR FILTER COVER, THAT HAD BEEN THE RESULT OF EXHAUST GASES BLOWING DIRECTLY ON IT. AN ENGINE RUN WAS PERFORMED AFTER THE AIR FILTER WAS REMOVED AND THE ENGINE RAN WELL AT ALL RPMS.