The certified flight instructor (CFI) indicated that he and his student pilot decided to land on the grass next to the runway because the student pilot “had no experience landing on sod.” The CFI stated that abeam the touchdown point they turned on the carburetor heat and that the approach was “normal but a bit low.” The CFI did not alert the student about the low altitude, assuming that they “could power over the tall grass and drop into the grass strip.” On short final the carburetor heat was turned off, and at an altitude of about five feet the student attempted to use power to maintain altitude. The engine did not respond and the student pilot did not reapply the carburetor heat. Subsequently, the airplane touched down short of the intended touchdown point. The CFI was unable to reach the controls prior to the aircraft nosing over. The CFI stated that he had previous experiences with the airplane failing to respond to throttle inputs during landing and that he should have known not to turn off the carburetor heat on short final. The aircraft sustained substantial damage to the fuselage and tail assembly. The CFI reported that there were no known mechanical malfunctions or failures prior to the accident. When plotted on a carburetor icing probability chart, the temperature and dew point fell within an area of the graph noting "Moderate icing cruise power or serious icing glide power."