The pilot stated that when he was 35 miles from his destination he reduced power to descend from 6,500 feet to 3,000 feet, and applied carburetor heat. When he added power to level off at 3,000 feet, the engine rpm stabilized between 1,800 to 2,000 rpm. The pilot stated that he suspected carburetor ice and applied carburetor heat again, but the engine did not regain full power. He diverted to a nearby airport and entered the pattern for the northern runway. During the landing sequence he determined that he was landing long. He applied power to perform a go-around, however, the engine only accelerated to 1,500 - 1,600 rpm. As he flew the airplane into a left turn to avoid trees the airplane stalled, entered a descent, and impacted a house. The carburetor icing chart indicated the possibility of serious carburetor icing at the reported temperatures. The Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25A) states that first indication of carburetor ice in an airplane with a fixed-pitch propeller is a decrease in engine rpm. Additionally, it states that when conditions are conductive to carburetor icing that carburetor heat should be applied immediately and should be left ON until the pilot is certain all the ice has been removed. If ice is present applying partial heat or leaving heat on for an insufficient time might aggravate the situation. Postaccident examination of the airframe and engine revealed no preimpact mechanical malfunctions or failure that would have precluded normal operation.