On April 6, 2016, about 1530 eastern daylight time, a Flight Design Gmbh CTSW, N466CT, was substantially damaged during a forced landing near Hilton Head Island, South Carolina. The sport pilot and one passenger were not injured. The airplane was registered to and operated by the pilot under the provisions of 14 Code of Federal Regulations Part 91 as a personal flight. Day, visual meteorological conditions prevailed, and no flight plan was filed. The flight originated from Cape Fear Regional Jetport (SUT), Oak Island, North Carolina about 1400, and was destined for Hilton Head Airport (HXD).The pilot reported that he was approaching HXD from the west, and reported to tower personnel that he was 8 miles out. He made a midfield call, retarded the throttle to 4,200 rpm, and descended from 1,300 feet above mean sea level (msl) to 1,000 feet msl. A few seconds after reducing the throttle, the engine "ran rough" for a few seconds, then shut down and would not restart. The pilot did not attempt to apply carburetor heat. He set up for best glide speed and maneuvered for a forced landing on a golf course. After landing, the left wing struck a tree and the airplane came to a stop. An inspector with the Federal Aviation Administration (FAA) responded to the accident site and examined the wreckage. The airplane struck a tree and came to rest upright. He observed structural damage to the composite leading edge of the left wing. The fuel system contained about 4.5 gallons of fuel. The fuel appeared to be free of contaminants and water. The air filter was clean and compression was observed on all cylinders. Following the examination of the engine and fuel system, the owner leveled the airplane and started the engine with the FAA inspector providing oversight. The engine started, produced power, and no discrepancies were noted. According to the 1550 weather observation at HXD, located about 2 miles southeast of the accident site, the temperature and dew point were 64 degrees F and 54 degrees F, respectively. According to the carburetor icing probability chart in FAA Special Airworthiness Information Bulletin CE-09-35 (Carburetor Icing Prevention), dated June 30, 2009, the temperature/dew point at the time of the accident was in the area of serious icing at glide power.