The student pilot reported that, during landing to a 40 ft wide runway, a wind gust pushed the airplane to the left. While correcting back to centerline, the flight instructor mentioned that they were slow, so the student added power. While on short final, the instructor told him to initiate a go around and to "go full power", and the student initiated a climb. He heard the stall warning horn and the instructor told him to "get the nose down." As the student lowered the nose, he felt a hard "bump" as the airplane touched down on the runway. The airplane veered left, struck vegetation, and spun around. The airplane sustained substantial damage to the left wing. The flight instructor reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The automated weather observation station, located about 11 miles north, reported that, about 10 minutes before the accident, the wind was from 190° at 9 knots. The student pilot landed the airplane on runway 17.