The pilot obtained a weather briefing before departing on a cross-country flight from West Bend, WI to Waseca, MN. Reportedly, the ceiling was 2500 to 3000 ft or better (as briefed) until after crossing the Mississippi River. The weather then began to deteriorate and the pilot encountered moderate turbulence. Subsequently, he flew into a misty condition that obscured his forward visibility. He found himself in a valley with the surrounding hilltops "nearly obscured" and elected to land in a harvested field. A downwind landing was made to avoid obstructions at the windward end of the field. After roundout, the aircraft continued to float, and when the pilot realized he was running out of room, he initiated a go-around. He applied power and retracted the flaps from full down to full up, but the aircraft's ability to climb and accelerate were negligible. To avoid hitting trees, the pilot elected to land in a river near the end of the field.