The pilot reported that the engine began to lose power during cruise flight. He applied carburetor heat and engine power was restored. Approximately 5 minutes later, the engine again began to lose power. The pilot applied carburetor heat and the engine power increased; however, the pilot was concerned the engine was not developing full power. He elected to make a precautionary landing on a road, but during the landing approach he noted power lines and a fence bordering the road. The pilot decided the road was not suitable for landing. Concerned that the engine was not performing well enough to execute a go-around, the pilot elected to continue the landing into a nearby cornfield. The airplane contacted the corn crop, a ditch, and a fence during the landing resulting in substantial damage to the wings and firewall. According to the Federal Aviation Administration icing probability chart, with the temperature and dew point, 84 degrees Fahrenheit and 75 degrees Fahrenheit respectively, conditions were conducive for carburetor ice at glide and cruise power.