On the downwind leg of the traffic pattern, the pilot receiving instruction and the flight instructor were having a conversation about when to extend the landing gear, as the pilot receiving instruction was new to this airplane. During this discussion, the pilots were contacted by air traffic control (ATC) and a conversation took place about a possible change of runway. After the exchange with ATC, the pilots did not return to their conversation about when to extend the landing gear. After being cleared to land, the pilot receiving instruction performed a normal approach to landing. The pilots reported that they realized they had forgotten to extend the landing gear when they heard the airplane contact the runway. The airplane skidded down the asphalt, resulting in substantial damage to the external longerons of the fuselage. The flight instructor reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation. The airplane was equipped with a landing gear position warning horn that was designed to sound when either of the throttles were pulled back for landing. Neither pilot specifically remembered hearing the warning horn during the accident landing. After the airplane was recovered, the landing gear warning horn was tested and was found to operate normally.