The 1,300-hour private pilot reported that during the initial takeoff climb, while at an estimated altitude of 75 to 80 feet above the ground, the engine RPM decayed to 1,950 RPM. Subsequently, the airplane's rate of climb was reduced to zero. The pilot responded by lowering the nose of the airplane and extending the flaps. With no remaining usable runway, the pilot turned the airplane to the left and elected to perform an emergency landing to a field. The pilot added that while maneuvering to avoid a fence, the airplane stalled, impacted the terrain and came to rest on its right side. The pilot, his 3 passengers and two small dogs were able to egress the airplane unassisted. The airplane was engulfed in flames a few minutes later. About 13 minutes after the mishap the weather reporting station 12 miles northeast of the accident site reported, the wind from 040 degrees at 13 knots, the temperature 57 degrees Fahrenheit, and dew point of 55 degrees Fahrenheit. According to information on a Carburetor Icing Probability Chart at the operating temperature/dew point, the airplane was found to be operating within the "serious icing at cruise power" range. Examination of the engine did not revealed any mechanical anomalies. Runway 35 was reported as a 3,800-foot long by 60-foot wide turf runway. The field elevation at the airport was reported at 3,615 feet and the density altitude was calculated at 4,347 feet. The estimated weight of the airplane at the time of departure was at its maximum takeoff weight of 2,300 pounds.