Probably a higher risk of carby icing from taking the engine to idle than a mixture cut
I doubt if carb ice would form to a significant degree in the less than 15 seconds it takes to close the throttle to simulate engine failure, have the student identify which engine has `failed` and for the instructor to then add a little power on that engine to simulate zero thrust (nominally around 12inches of manifold pressure).
Following the Air North Brasilia fatal crash at Darwin where the check pilot pulled back the throttle to simulate engine failure shortly after lift off, CASA mandated that all future emergency training in certain types of aircraft (practice engine failure on take off), must be conducted in an approved flight simulator. This mandate recognised the risks involved with any deliberate low altitude engine failure practice.
The history of these type of accidents due to mis-handling of practice engine failures in multi-engine aircraft, goes back many decades. Indeed, a fatal crash at Camden in a de Havilland Dove in the 1950's was caused by the then common practice of not only pulling the mixture but actually feathering the prop. A senior DCA Examiner of Airman was killed in that crash while the instructor lost an eye. Clearly the instructor took the chance that everything would work out OK and tragically it didn't.
Let's not be coy about all this. Pulling the mixture fails the engine dead and the prop immediately windmills creating drag that will prevent a positive rate of climb. That is why the feathering propeller was designed in the first place. So the instructor has created an immediate serious emergency when there was nothing wrong with the engine in the first place.
If the instructor is so enthusiastic as to create a real emergency shortly after lift off in order to show off to his student how realistic the situation has become, maybe he should spare the time one day to speak to the relatives of those who have lost their lives in the push for realism. I doubt if he would receive much admiration from them for his actions.
Of course asymmetric training is a requirement; but I would have thought that common sense (good airmanship) would dictate caution when dicking around with practice engine failures near the ground, where the room for error is small. There will always be macho personalities among certain types of instructors who, in their misguided and even reckless enthusiasm, will risk the lives of their students in order to demonstrate realism. Wiser heads will have learned from the lessons of the past and realise there is a limit to realism, beyond which is sheer idiocy. Some may argue mixture cuts at low level fall into the latter category.