The student pilot was receiving instruction in the procedures associated with an engine failure after take off. At 1000 feet above ground level carburettor heat was applied, the throttle retarded to idle and the aircraft configured for descent. At 800 feet the power was reapplied, carburettor heat was selected off and the aircraft climbed back to repeat the lesson. After the second exercise the engine would only develop 1500 rpm and was running roughly. The instructor took over, exercised the carburettor heat and left it on, but there was no improvement in engine performance. He then carried out a forced landing in a paddock. During the latter part of the landing run the nosewheel dug into the soft surface, and the right wing was damaged. The weather conditions at the time (ambient air temperature 16-17 with a dew point of 11 and overcast) were favourable to the formation of carburettor ice. The engine had recently been overhauled. The operator reported that the aircraft normally gave only a very small drop in rpm when carburettor heat was applied. The spark plugs were found to be heavily sooted with a fresh carbon deposit, which indicated that the engine had suffered a rich cut. This is consistent with the effects of ice accumulating in the carburettor. The carburettor heat box was found to be loosely fitted to the carburettor and one side of the box had a rubber seal missing. This resulted in a loss of effectiveness of the carburettor heating system.