WHILE ON A DOWNWIND FOR A LANDING IN MULTI-ENGINE TRAINING, THE NOSE GEAR WOULD NOT EXTEND. ALL EFFORTS TO EXTEND THE NOSE GEAR, INCLUDING A BOUNCED LANDING, WERE UNSUCCESSFUL. THE AIRCREW INTENDED TO LAND ON THE MAIN GEAR AND THEN HOLD THE NOSE OFF UNTIL THE AIRCRAFT SLOWED. THE MULTI-ENGINE INSTRUCTOR (IP), WHO OCCUPIED THE RIGHT SEAT, ESTABLISHED THE AIRCRAFT ON A STRAIGHT-IN FINAL APPROACH WITH 1/2 FLAPS AND ZERO THRUST (10 IN HG) ON BOTH ENGINES. WHILE STILL AIRBORNE, THE IP COMMANDED THE STUDENT (A SINGLE-ENGINE IP) TO FEATHER BOTH PROPELLERS AND SHUT DOWN BOTH ENGINES. IMMEDIATELY THE RATE OF DESCENT INCREASED AND THE PLANE TOUCHED DOWN ON AN EMBANKMENT ABOUT 45 FT SHORT OF THE RUNWAY. THE PLANE BOUNCED, AND AFTER A SECOND TOUCHDOWN, THE NOSE CONTACTED THE RUNWAY ABOUT 55 FT BEYOND THE TOUCHDOWN POINT AND WAS DAMAGED. AN INVESTIGATION REVEALED THAT A ROCKING NUT WHICH RETAINED THE NOSEWHEEL, WAS MISSING. THE AIRCRAFT HAD UNDERGONE A 100 HR INSPECTION ABOUT 8 HOURS PREVIOUS TO THE ACCIDENT.