The pilot reported that during landing, the airplane encountered a wind gust that yawed the airplane left. The pilot applied full throttle, turned off the carburetor heat, and initiated a go-around, but did not retract the flaps. The airplane continued left as the pilot attempted to climb, but ultimately it collided with trees and then terrain. The airplane sustained substantial damage to the fuselage and both wings. An examination of the airplane at the accident site showed that the wing flaps were extended at least 30°. The pilot reported that there were no mechanical malfunctions or anomalies with the airplane that would have precluded normal operation. The airplane flight manual states that during a botched landing or go-around, the flaps should be retracted to 20° after full power is applied and should remain between 10° and 20° until obstacles are cleared.