The pilot reported that after a 1.5-hour pleasure flight, he entered the traffic pattern for landing. He reduced power to idle and applied carburetor heat. He turned onto the base leg and then onto final approach. The pilot noted the airplane was too low and attempted to add power, but there was no response from the engine. The airplane touched down short of the runway, impacted the airport's chain link perimeter fence, nosed over, and came to rest inverted. The pilot reported that he was in a glide with the power at idle for about 30 seconds and that he did not clear the engine during the glide. The reported temperature and dew point at the airport were 3 and -2 degrees Celsius, respectively. Plotting these values on a carburetor icing chart indicated the airplane was operating in conditions conductive to serious icing at descent power.