The pilot was on a cross country flight and at the destination airport entered the right downwind leg of the airport traffic pattern, then turned onto right base leg of the airport traffic pattern. Because of “excessive wind gusts” on final approach he performed a go-around and remained in the traffic pattern for the same runway. On final approach the flight again encountered a wind gust and the airplane descended. He added power to arrest the descent but the airplane then floated down the runway. The airplane touched down just prior to a taxiway, with about 959 ft of runway available. He applied the brakes but realized he would be unable to stop before the runway end. He applied power to abort the landing, but the airplane did not climb as he expected and it travelled off the end of the runway into a farm field. He did not recall if he applied the brakes or reduced power in an attempt to abort the aborted landing. The airplane impacted a metal frame that enclosed plants and came to rest with the nose landing gear collapsed. The engine mount was substantially damaged. He reported that when he added full power to go-around the engine responded, the airplane was decelerating with initial brake application, and there was nothing mechanically wrong with the airplane that resulted in the runway excursion. Postaccident examination revealed the flap selector was in the retracted position.