THE PILOT RECEIVED A WEATHER BRIEFING BEFORE THE FLIGHT DURING WHICH A POSSIBLE CHANCE OF A LITTLE BIT OF ICING AT 6000 FEET WAS MENTIONED. DURING THE FLIGHT AT ALTITUDES OF 4,000 FEET AND BELOW, THE AIRCRAFT PICKED UP HEAVY ICING. THE PILOT WAS UNABLE TO LOCATE THE AIRPORT DURING THE VOR APPROACH SO HE MADE A TURN BACK TOWARD THE AIRPORT IN AN ATTEMPT TO GAIN VISUAL CONTACT. THE PILOT REPORTED THAT DUE TO THE AMOUNT OF ICE ON THE AIRPLANE, HE WAS UNABLE TO MAINTAIN ALTITUDE WITH FULL POWER. AN OFF AIRPORT LANDING WAS MADE DURING WHICH THE AIRPLANE CONTACTED TREES.