The pilot reported that he was on a local flight and the engine gradually lost power. He performed the checklist for a loss of engine power and the airplane did not regain full power. The pilot stated that he picked a landing field, extended full flaps, and then the engine "quit." He pumped the throttle, the engine restarted, and he started to climb the airplane. The engine lost power again. The pilot picked another field and the airplane nosed over during the forced landing. The field contained corn. The airplane was recovered and the engine ran during a subsequent test run. The pilot reported that a cup of water was removed from the right fuel tank sump and a quarter cup from the front sump during the airplane preflight. The local airport's temperature and dew point were plotted on the carburetor icing chart listed in Special Airworthiness Information Bulletin CE-09-35. Their intersection fell in the “serious icing (glide power)” range.