The pilot stated that while crossing Lake Huron at an altitude of 3,000 feet, the engine began to lose power. The pilot contacted flight watch and informed them of the situation. He moved the fuel selector handle and enriched the fuel mixture to no avail. The pilot stated he applied carburetor heat, moved the throttle, and fuel selector switch again, but by this time he was about 100 feet above the water and 15 to 17 miles off shore. He contacted flight watch again to provide a position update and to tell them he was ditching in the lake. The pilot stated that engine power was regained just prior to the airplane contacting the water; however, by that time he was unable to avoid the ditching. The pilot exited the airplane which sank soon after contacting the water. The pilot was able to tread water for approximately 18 hours prior to be picked up by a pleasure boat. The pilot was hospitalized for several days following the accident. The airplane remains at the bottom of Lake Huron in about 210 feet of water. The outside air temperature was 73 degrees Fahrenheit and the dew point was 57 degrees Fahrenheit. According to the FAA Icing Probability Chart, these conditions were conducive for serious icing at glide power. The pilot reported he did not recognize the symptoms of carburetor ice and that he should have applied the carburetor heat sooner.