The pilot stated that he had obtained a full weather briefing and an IFR clearance from Grand Marais, Minnesota to Des Moines, Iowa prior to departure; and that the flight was uneventful, except for stronger than forecasted headwinds aloft. Enroute, the pilot further stated, he received two in-flight weather advisories but decided to continue on to DSM. According to the National Weather Service, forecasted--and known--icing conditions existed throughout the route of flight. Several FAA weather briefing personnel stated that the pilot was warned of icing conditions on all of his contacts with FSS. Only when the aircraft began picking up rime ice did the pilot request vectors to a nearby airport for a precautionary landing. The aircraft landed nose first as the pilot reduced power over the runway threshold--the nose gear collapsed upon impact, damaging the propeller and engine mounts. A post-accident inspection of the aircraft revealed the presence of ice along the leading edge of the wings.