The certified flight instructor (CFI) stated that after takeoff he flew to another airport and demonstrated to the student a simulated loss of engine power by reducing power then applying carburetor heat. He began a right descending turn and reported clearing the engine (verifying full engine power was available) at least one time during the descent but added that he should not have left the engine at a low idle condition for more than 1 minute. He approached runway 02 and lowered 10 degrees of flaps while on a short base. The approach appeared normal to slightly high, and on short final (about 100 feet above touchdown zone elevation), the flight encountered a very strong and turbulent gust/rotor that necessitated immediate full power. He applied power and later reported the engine hesitated or stumbled. He removed carburetor heat, and pushed forward on the throttle and mixture controls, and also pumped the throttle in an effort to restore engine power which was unsuccessful. He maneuvered the airplane to a clear space and landed in a wooded area. Inspection of the engine by a Federal Aviation Administration (FAA) airworthiness inspector following recovery of the airplane revealed no evidence of preimpact mechanical failure or malfunction. A surface observation weather report approximately 17 minutes before the accident, indicated the temperature and dew point were 18 and 13 degrees Celsius respectively, (64 and 55 degrees Fahrenheit),. According to a FAA Special Airworthiness Information Bulletin (SAIB) CE-09-35, dated June 30, 2009, the temperature and dew point were favorable for serious icing at glide power.