The airplane incurred minor damage while landing at about 1205 Eastern time. The airline transport pilot and commercial pilot were not injured. Visual conditions prevailed. During a go-around following a practice instrument approach, the crew retracted the landing gear. However, a controller advised the landing gear appeared to be in the extended position. The pilots then selected the landing gear to the extended position and noted correct gear-extended cockpit indications. During a subsequent landing, the nose landing gear collapsed and the airplane slid to a stop on the runway.