The student pilot stated that when he entered the destination airport traffic pattern for landing, there were strong wind gusts that were not on the automated weather observing system report. He said the airplane’s descent during the approach was stable, so he decided to continue the approach for landing. He said that shortly after the airplane’s nose wheel landing gear touched down on the runway, the airplane caught a strong wind gust that resulted in a weathervane effect and a sharp change in its direction to the right. He then applied left rudder control input, but the airplane veered to the right and off the runway where it impacted terrain. The airplane sustained substantial damage to the fuselage. The pilot stated there was no preaccident failures or malfunctions the airplane that would have precluded normal operations.