According to the flight instructor, the wind was gusting significantly during the practice short field landing with the student pilot. He described that the student pilot made a normal approach, but as they got over the runway and attempted to land and entered ground effect, the airplane ballooned and turned sideways, which was exacerbated by the winds. The student pilot added power but did not input sufficient rudder control to straighten the airplane’s flight track. The airplane continued to float as the student increased engine power rapidly, then the student “froze” as the airplane began to turn further sideways over the grass. The flight instructor took control of the airplane, added full power, and attempted a go around but was unable to regain directional control and stop the descent. The airplane landed hard in a marshy area off the side of the runway, substantially damaging the wings and fuselage. The flight instructor reported that there were no preimpact mechanical malfunctions or failures of the airplane that would have precluded normal operation.