The pilot reported that she departed on the 1-hour cross country flight with 26 gallons of fuel on board. The pilot said that her cruise altitude varied between 2,500 and 3,000 feet mean sea level (msl). As the airplane approached the destination airport, she reduced engine power to approximately 2,300 rpm in order to descend to traffic pattern altitude. During the downwind leg, a reduction of engine power to 2,000 rpm was made to slow the airplane to approach airspeed. As she initiated a turn to base leg, a final reduction of engine power was made and the carburetor heat was activated. During the turn to base leg, the engine began to lose engine power. The loss of engine power was reported to be gradual, not instantaneous, occurring over a period of approximately 5 seconds. The engine did not respond to throttle and mixture control movements. The pilot stated that the loss of engine power occurred 700-800 feet above ground level (agl) while on base leg. She said that she was worried about stalling the airplane, and established a descent to remain above stall speed. The airplane landed in a grass area about 50 feet short of the runway. Shortly after touchdown the nose gear collapsed and the airplane came to an abrupt stop. The temperature and dew point in the vicinity of the accident site were 17 degrees and 12 degrees Celsius, respectively. Data indicated the possibility of moderate carburetor icing at cruise power and serious icing at descent power under those conditions.