The private pilot reported that, during the local pleasure flight, the engine started to run roughly and that he thought that it was due to carburetor ice. The pilot applied carburetor heat, and after about 3 minutes, the engine still did not seem like it was running smoothly. The pilot initiated a climb; however, the airplane would not gain altitude, so he chose to make a precautionary landing on a sandbar in a river. After touchdown on the rough and bumpy surface, the pilot applied braking action. The wheels dug into the soft sand, and subsequently the airplane nosed over and came to rest inverted. The wings and the left lift strut were substantially damaged. The pilot reported that there were no preaccident mechanical failures or malfunctions with the engine or airplane that would have precluded normal operation. The nearest weather reporting facility, located about 27 nautical miles northwest of the accident site, reported that, about the time of the accident, the temperature was 30°F and the dew point was 16°F, which was near the range of atmospheric conditions being conducive to icing at glide and cruise power settings. .