THE ENG QUIT WHEN A STUDENT PLT TRIED TO GAR AFTER BOTCHING A SIMULATED ENG EMER.

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I PULLED THE CARB HEAT ON AND REDUCED PWR TO ABOUT 1200 RPM TO PRACTICE A SIMULATED ENG FAILURE. WE WERE DIRECTLY OVER THE BIG LAKE AIRSTRIP; SO I INSTRUCTED HIM TO MAKE HIS APCH TO THAT FIELD. AS HE ENTERED L DOWNWIND FOR THE E RWY; I CLRED THE ENG. I DID NOT CLR THE ENG AGAIN DURING THE APCH. THE STUDENT'S PATTERN WAS WIDE. WHEN WE TURNED TO FINAL AT ABOUT 500 AGL; WE WERE TOO FAR AWAY TO MAKE THE FIELD. BOTH THE STUDENT AND I RECOGNIZED THIS. I INSTRUCTED HIM TO INITIATE A GAR. AS HE WAS PUSHING IN THE THROTTLE; HE ENTERED A VERY SHALLOW R BANK. I DID NOT CORRECT THE BANK OR TELL THE STUDENT TO DO SO WHEN I FIRST NOTICED IT. HE WAS AN ADVANCED STUDENT PREPARING FOR HIS PVT CHKRIDE. I DIDN'T FEEL I SHOULD IMMEDIATELY CORRECT EVERY SMALL ERROR HE MADE. THE ENG DIDN'T RESPOND TO THE THROTTLE. WHEN I REALIZED WHAT WAS HAPPENING; I TOOK THE CTLS; CORRECTED THE BANK AND AIMED FOR THE ONLY CLRING I SAW. THE AIRSTRIP WAS TOO FAR AWAY TO BE CONSIDERED AS AN OPTION. I INITIATED THE RESTART PROCS; BUT DID NOT COMPLETE THEM. I NOTICED MY AIRSPD GETTING TOO SLOW AND THE TREES BELOW APCHING RAPIDLY. I CONCENTRATED MY EFFORTS ON MAINTAINING BEST GLIDE SPD OVER THE TREES TO THE CLRING. THE LNDG GEAR CLIPPED THE TOPS OF THE TREES JUST BEFORE THE CLRING. I LANDED AS SLOWLY AS POSSIBLE; TAIL LOW. THE NOSE GEAR HIT A BERM AND COLLAPSED. THE ACFT SLID ON ITS NOSE A SHORT DISTANCE UNTIL IT HIT ANOTHER BERM AND ROLLED OVER NOSE FIRST. WE STOPPED UPSIDE DOWN. NEITHER OF US WAS HURT -- NOT EVEN A BRUISE OR SCRATCH. THE EMER LOCATOR XMITTER WAS NOT AUTOMATICALLY ACTIVATED. ANY ENG; BUT PARTICULARLY THE CONTINENTALS OF CESSNA 150'S; NEEDS TO BE PAMPERED IN VERY COLD WX. THE TEMP IN THE PRACTICE AREA WAS 10-15 DEGS COLDER THAN AT THE POINT OF DEP. I PROBABLY HAD THE THROTTLE SET TOO LOW FOR THOSE CONDITIONS. I'VE BEEN TOLD SINCE THAT 1500 RPM IS THE LOWEST SAFE SETTING IN WINTER. THE STUDENT TOLD ME LATER THAT HIS INSTRUCTOR HAD ALWAYS TOLD HIM TO TURN OFF THE CARB HEAT AND THEN ADD THE PWR. IN WARMER CLIMATES; THAT'S NOT A PROB. IN AK; IT IS. HE MAY HAVE TURNED OFF THE CARB HEAT BEFORE ADDING PWR. ANOTHER STUDENT WHO HAD BEEN FLYING THAT ACFT LATER SAID THAT IT HAD BEEN RUNNING ROUGH AND BACKFIRING ON TOUCH AND GOES AND GARS (HE ALWAYS ADDS PWR FIRST AND THEN TURNS OFF THE CARB HEAT). A MECH WHO HAD WORKED ON THAT AIRPLANE SAID THAT THE IDLE MIXTURE MAY HAVE BEEN SET TOO LEAN.