The instructor reported closing the throttle to simulate an engine failure during a training flight. The student added carburetor heat first, instead of establishing a proper glide. The instructor removed carburetor heat and advised the student of the desired sequence. The instructor added carb heat, opened the throttle slightly, and cleared the engine during descent. The student selected a field for the simulated forced landing. The instructor added power to recover at 300 ft AGL. The engine accelerated to partial power then 'cut out.' The instructor tried twice more to restore full power to no avail. A forced landing was made in a beet field, 10 miles southwest of the destination. At touchdown, the nose wheel hit a ditch and was sheared off. The aircraft traveled 200 feet, nosed over, and came to rest inverted. A post accident engine run by an FAA inspector failed to reveal evidence to explain the reported loss of power. The temperature was 41, and the dew point was 27.