On July 14, 1996, at 1350 eastern daylight time (edt), a Piper PA-28, N4798F, registered to Aretz Flying Service, Inc., of Lafayette, Indiana, and operated by a private pilot, ran off runway 25 (2812' x 50' dry/asphalt) after experiencing a crosswind on touchdown at Aretz Airport, Lafayette, Indiana. The airplane sustained substantial damage when it collided with trees. The pilot and passenger reported no injuries. The personal 14 CFR Part 91 flight was operating in visual meteorological conditions. No flight plan was on file. The flight departed Lafayette, Indiana, at 1305 edt. According to the pilot's written statement, the airplane was on a VFR flight plan from Lafayette, Indiana, to Meig's field in Chicago, Illinois. He was advised by flight service of heavy rains along his flight path. The pilot saw the heavy rains and cancelled his flight plan. He decided to return to the Lafayette Airport before the adverse weather moved in. The pilot stated that he used full flaps (40 degrees) on final approach because the airplane was high. The pilot reported that a wind gust pushed the airplane off the left side of the runway just prior to touchdown. He continued to report, "...airspeed was approximately 60 knots at the end of my flare. I gave it full power and lowered one notch of flaps [raised flaps to 25 degrees] but the plane wouldn't climb. The airspeed was so slow that I had no directional control and headed for the trees... ." The airplane flew across a soybean field and impacted a line of trees on the left side of the runway. The pilot reported the winds 300 degrees at 13 knots.