The pilot reported that he performed a preflight inspection and run-up of the airplane prior to takeoff. After takeoff, when the airplane was about 250 to 300 feet above ground level the airplane's engine lost power. The pilot reported that he applied carburetor heat but could not maintain altitude and struck trees. The pilot reported that he believed that the engine power loss was due to carburetor icing. The weather conditions at the time of the accident included a temperature of 25 degrees Celsius, and a dew point of 13 degrees Celsius, which according to a carburetor icing probability chart, was in the range of susceptibility for serious icing at descent power settings, and moderate icing at cruise power settings.