The 485-hour flight instructor and the 11-hour student pilot were executing a crosswind landing during a local training flight. Shortly after touch down on Runway 17R, the nose landing gear collapsed, and the airplane began to skid down the runway. While attempting to bring the airplane to a stop, the propeller and left wing contacted the ground. The winds at the time of the mishap were reported from 180 degrees at 11 knots. An examination of the airplane by an Federal Aviation Administration (FAA) inspector revealed that the axel for the nose landing gear was missing and it was later located along the centerline of the runway. The lock nut securing the axle to the landing gear assembly was not located, and it was not determined why the nut was not in place. The last annual inspection was completed on October 24, 2005, about 22.2 hours prior to the mishap. No recent maintenance was reported on the nose landing gear assembly.