On October 17, 1997, about 1730 eastern daylight time, a Cessna 172G, N4690L, registered to individuals, collided with trees while making a forced landing following loss of engine power near Panacea, Florida, while on a Title 14 CFR Part 91 instructional flight. Visual meteorological conditions prevailed at the time and no flight plan was filed. The aircraft received substantial damage and the student-rated pilot was not injured. The flight originated from Panacea, the same day, about 1630. The pilot stated that he climbed to between 1,800 and 2,300 feet after departure and performed maneuvers. The engine began to run rough during this time and the oil pressure, oil temperature, and rpm were fine. He continued the flight and descended to 1,200 feet to perform more maneuvers. While maneuvering he noticed that the engine had lost 100 rpm and he applied carburetor heat, but nothing happened. The altitude was now 700 feet and he increased the engine throttle to full. The engine quit. Attempts to restart the engine were unsuccessful and finding no suitable place to land, he landed in trees. The aircraft descended through the trees and came to rest. Examination of the aircraft after the accident was performed by an airframe and powerplant mechanic. The carburetor heat was found in the off position and all engine controls were properly attached and operating normally. After recovery of the aircraft from the trees, the engine was test run under the supervision of an FAA inspector. The engine started immediately and after warming up was operated to 1,500 rpm. The magnetos operated normally during checks and the carburetor heat operated normally. No evidence of mechanical failure or malfunction was found during the test run. A higher rpm was not selected due to vibration observed from the bent propeller blades. (See attached statements). Carburetor icing probability curves showed that at the time of the accident the aircraft was operating in conditions conducive to visible icing at glide and cruise power and serious icing at glide power. (See attached icing probability curves).