The pilot reported that during the landing roll he felt as though the airplane was being pushed to the left side of the runway and he applied full right rudder and left aileron. The airplane exited the left side of the runway, and he added power to prevent the airplane's nose from colliding with a drainage culvert, but the airplane accelerated and impacted a tree. The airplane sustained substantial damage to the leading edge of the left wing. The pilot reported that there were no mechanical malfunctions or failures with the airplane that would have precluded normal operation. The pilot reported that the wind at the destination airport was 090 at 10 knots gusting to 15. The nearest weather reporting station, located 14 miles to the north at the departure airport, reported about the time of the accident the wind was from 040 at 3 knots. The airplane landed runway 24. The pilot landed to runway 24 because of the 2.9 percent uphill gradient.