At about 09:43 EST, the pilot of a Piper PA-28-181 lost directional control and struck trees while taxiing at Ocean Reef Club Airport. There were no injuries. The pilot said that, while he was on the downwind leg for runway 04, he was advised by Unicom that the wind was gusting to 18 knots from 330 degrees. He continued the approach and heard the crew of a Falcon announce that they were 10 miles out and would advise when they were on the downwind leg. The Piper landed uneventfully and rolled of the way down the runway. The pilot veered to the right near the right edge of the runway then made a 90-degree turn to the left and stopped. He looked for the Falcon airplane but did not see it, and made a second 90-degree turn and began taxiing down the runway. While he was taxiing, the airplane suddenly veered off the left side of the runway into trees.