The pilot stated she had been conducting parachute drop operations through out the day. She would depart St. Mary's Airport climb to 11,000 feet, drop the skydivers, descend at 170 knots, land, add fuel or take on more jumpers, and depart again. The pilot departed on the last parachute drop flight at an undetermined time, completed the parachute drop, and descended with power on. The pilot did not apply carburetor heat during the descent because the carburetor heat control cable was stuck, and would not move for the last two days. The pilot entered the traffic pattern for Runway 13 on a right base leg, and completed the before landing check. The pilot turned final at 500 feet. and the airplane experienced a total loss of engine power. The pilot checked the magnetos to ensure the magnetos were on the "both" position, established a glide, and verified the fuel selector valve was in the "both" position. The pilot realized she could not make the runway and made a forced landing adjacent to the airport. The airplane collided with the tops of 60 foot trees. The nose of the airplane pitched down, and the airplane collided with the ground in a left wing low nose down attitude. The airplane received structural damage to both wings and the empennage. The pilot unfastened her seatbelt and shoulder harness and exited the airplane through the broken front windshield with minor injuries. The pilot informed an FAA inspector that she had performed maintenance on the carburetor heat control cable by applying a silicone coating to the cable. The cable worked about two days and stuck again. The pilot does not hold a mechanics certificate with ratings for airframe and power plant. No entry was made in the airplane log book concerning the maintenance on the carburetor heat control cable. The nearest weather reporting system to the airport was Jacksonville International Airport, Jacksonville, Florida, located 17 nautical miles southwest of the airport. The 1456 surface weather observation was wind 170 degrees at 17 knots gusting to 15 knots. Few clouds at 4,000 feet, broken clouds at 2,500 feet, temperature 88-degrees Fahrenheit, dew point temperature 61 degrees Fahrenheit, and altimeter 29.90. The field elevation at St. Mary's Airport is 24 feet. Review of the icing probability chart indicates at a temperature of 88 degrees Fahrenheit and a dew point temperature of 61 degrees Fahrenheit the airplane will encounter serious icing conditions at glide power. Review of the Cessna Skylane and 182 Owner' s Manual states, "During climb, watch the engine for any sign of icing-roughness or loss of manifold pressure. Remember, icing will not produce a drop in rpm after you have set up climb power, since the propeller will change pitch to compensate for the power loss. If the engine begins to ice, apply full carburetor heat at once. Review of the Cessna Operating Check List on page 2-5 states in "LET-DOWN (3) Apply sufficient carburetor heat to prevent icing, if icing conditions exist." Review of the FAA Approved Airplane Flight Manual Supplement for the airplane revealed STC No. SA01944CH had been issued for the use of unleaded automotive gasoline or 82 UL avgas on March 2, 2004. The Flight Manual Supplement states on page 18, (4) "Carburetor Ice, When using unleaded automotive gasoline, the onset of carburetor ice may occur earlier under the same atmospheric conditions when using 80/87 minimum grade aviation gasoline. There is no change in the techniques for recognizing and correcting for carburetor ice." The airplane was released to the registered owner on April 18, 2007.