The instructor pilot stated that he and his student had departed on a VFR cross country training flight. While enroute to their destination he initiated a simulated engine failure near an enroute uncontrolled airport. He stated the winds were variable and estimated to be about 8 knots from the northwest. The instructor said that the student was flying the airplane until he took over to align the airplane with the runway centerline. The instructor extended 30 degrees of flaps and completed the touch and go landing. He said after applying full power he pushed the carburetor heat off and retracted the flaps. At about 50/60 feet he stated that the airplane's engine lost power. The pilot entered a forced landing with partial engine power. The airplane overshot the 3240 feet long runway to the left side and during landing roll, collided with a fence. According to a standard carburetor icing probability chart, the temperature and dew point were located in the moderate icing-cruise power or serious icing-glide power area of the chart.