On January 31, 2006, about 1025 Pacific standard time, a Cessna 172N, N492SF, registered to and operated by Snohomish Flying Service as a 14 CFR Part 91 local instructional flight, experienced a loss of engine power shortly after takeoff from Harvey Field, Snohomish, Washington. During the off airport landing in a flooded pasture, the airplane nosed over. Visual meteorological conditions prevailed at the time and no flight plan was filed. The aircraft was substantially damaged and the flight instructor and airline transport pilot receiving instruction for an add-on rating/certificate were not injured. Both pilots reported that shortly after takeoff, the engine lost power after the aircraft attained an altitude of about 250 to 300 feet above ground level. The flight instructor took over the flight controls and accomplished an off airport landing in an open field that was flooded by recent rains. During the landing roll, the airplane nosed over. The wings and a lift strut were damaged, fuel was leaking from the fuel tank(s), and the top of the vertical stabilizer was crushed. On February 1, 2006, a Federal Aviation Administration Inspector from the Seattle, Washington, Flight Standards District Office, witnessed the start and run-up of the engine after the wreckage had been recovered from the field. The inspector reported that after the fuel system was flushed out, the engine was started, and after a few minutes ran smoothly. The rpm was increased to 1800 and a magneto check was accomplished with no abnormalities noted. The engine was run for about 5 minutes and then shut down. No evidence of a mechanical failure or malfunction was noted during the engine run. At 0953, the weather facility at Everett, Washington, Paine Field located 6 nautical miles to the west was reporting a temperature of 42 degrees F, and dew point of 36 degrees F. The carburetor icing probability chart indicated that for the reported temperature and dew point, the aircraft was operating in probable serious carburetor icing conditions at cruise or climb power.