The operator reported that the student pilot was cleared by air traffic control to taxi behind another airplane. While taxiing, the other airplane witnessed the student pilot turn the airplane off the taxiway, taxi through a row of hangars, and onto the main vehicle access road that led into the airport. The student pilot then attempted to taxi the airplane through an access gate (for cars) that was too narrow for the airplane, and both wings struck the gate posts which resulted in substantial damage to both wings. An airport rescue and fire fighter asked the pilot to recount the moments before impact with the gate. The student pilot stated, “to be honest, I forgot I had wings.” The operator reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.