On June 2, 2022, about 1803 central daylight time, a Cessna 172P, N65497, was substantially damaged when it was involved in an accident near Ennis, Texas. The flight instructor and pilot were not injured. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 instructional flight. While enroute to the Ennis Municipal Airport (F41), the flight instructor reported that the engine power decreased about 200 rpm on two occasions. The pilot flew an approach to Runway 16 at F41 and executed a go-around due to excess airspeed. When the throttle and carburetor heat controls were advanced to the full forward position, the engine power only increased to about 2,000 rpm. The flight instructor adjusted the mixture control and reapplied carburetor heat in an attempt to increase engine power, but the power decreased, and the flight instructor executed a forced landing to a field. During the landing roll, the flight instructor turned right to avoid cows and the airplane impacted a tree, which resulted in substantial damage to the right wing. The postaccident examination of the engine revealed normal engine continuity and no anomalies were observed with the carburetor. Four hold down studs on the No. 1 cylinder were fractured and their separated pieces were found in the bottom of the cowling. No other anomalies were observed that would have precluded normal engine operation. No impact damage occurred in the vicinity of the engine All spark plugs had signatures consistent with normal engine operation when compared to a Champion Check-a-plug chart. The weather conditions at the time of the accident were conducive to serious carburetor icing at glide power.