The pilot reported that he and his two passengers departed during visual meteorological conditions on a cross country flight. About 55 miles from his departure point he said the ceiling decreased to 300 feet and visibility was one half mile in snow showers. He said the temperature was 38 to 49 degrees Fahrenheit. He turned the engine anti ice on. He flew another 6 to 8 miles and noted the temperature as 40 to 41 degrees. He turned the anti ice off. The front seat passenger checked the engine inlet area and reported to the pilot that she did not see anything. In less than one minute the engine lost total power. The pilot entered an autorotation and tried to land in an open area. He said he had to use some collective pitch to clear trees. With insufficient remaining collective pitch, the helicopter landed hard. After the accident, the engine was started on scene. Under the supervision of an FAA safety inspector it was also ran through all power settings without difficulty at a test facility. The pilot said he did not have the engine air induction particle separator kit installed on the aircraft, as required by the Bell 206B flight manual. The manual also states the engine anti ice should be 'on' in visible moisture when the temperature is below 40.