The pilot reported that he had applied carburetor heat intermittently during the flight, but that during the final descent to the destination airport, he did not. The engine stopped producing power, and during the subsequent forced landing the airplane collided with trees which resulted in substantial damage to the fuselage. The pilot reported that there were no mechanical deficiencies with the airplane that would have precluded normal operation, and stated that the engine stopped producing power due to carburetor icing. Interpolation of a carburetor icing probability chart revealed that atmospheric conditions at the time of the accident were conducive to serious icing at all power settings.