The pilot reported that while enroute, flying below a 1000-foot ceiling in 2 miles of visibility and light snow, he encountered various instances of carburetor icing which were resolved using the periodic application of carburetor heat. However, later in the flight, he encountered carburetor icing that wasn’t clearing with the application of carburetor heat. The pilot elected to make an off-airport landing and while performing a descending 180° turn, maneuvering to land, he reported that the airplane’s engine lost all power. The pilot leveled the airplane’s wings partway through the turn and landed straight ahead, in a small clearing. The airplane overran the landing area and impacted a clump of trees which resulted in substantial damage to the wings. According to the Carburetor Icing Probability Chart (FAA SAIB CE-09-35), the atmospheric conditions at the time of the accident were conducive to carburetor icing at cruise power and glide power. According to FAA Advisory Circular 20-113, "To prevent accidents due to induction system icing, the pilot should regularly use [carburetor] heat under conditions known to be conducive to atmospheric icing and be alert at all times for indications of icing in the fuel system." The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.