The airplane veered off the runway during the landing roll. The student pilot decided to perform touch-and-go practice takeoff and landings after arriving at his destination airport. On the third landing the main landing gear touched down first with the nose landing gear following shortly thereafter. As he reached his hand over to raise the flap lever to the "up" position, the airplane encountered a gust of wind. The airplane veered off the right side of the runway and collided with a gate. The airplane incurred damage to the right strut. The pilot initially suspected a disconnect of the rudder cables. A mechanic inspected the entire rudder control system and noted no anomalies or malfunctions that would have precluded normal operation. In a later statement, the pilot reported no preimpact mechanical malfunctions or failures with the airplane. The sole wind information provided at the airport was via a windsock. The pilot estimated that the winds were variable at 5 knots with slight gusts.