The student pilot reported that he was preparing for his private pilot check ride and after about 90 minutes of flying, he approached the airport and entered the traffic pattern for runway 21, a 2,205 ft-long runway. While established on "short final," he elected to perform a go-around because he was not "comfortable" with the approach. On the second landing attempt, the airplane floated past the intended touchdown point, before landing on the runway, and the student pilot was unable to stop the airplane before it went off the departure end. Subsequently, the airplane struck a perimeter fence and an embankment, which resulted in the nose landing gear collapsing and substantial damage to the fuselage and left wing. The student pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation. The winds reported at an airport 4 miles east of the accident location were from 320 degrees true at 7 knots.