THE ACFT WAS ON A FLT FROM PITSBURG, PA TO SALINA, KS WITH AN EN ROUTE STOP AT ST LOUIS, MO. DURING A BRIEFING AT PITSBURG, THE PLT WAS ADVISED OF A NOTAM THAT THE NORTH 6800 FT OF RWY 17/35 WAS CLOSED, RWY LIGHTS OBSCURED, 10 FT SNOWBANKS. HE DID NOT GET A BRIEFING DURING THE STOP-OVER AT ST LOUIS. DURING AN INSTRUMENT APPROACH TO SALINA, HE CONTACTED THE FSS AND REQUESTED AN ARPT ADVISORY. AN ADVISORY WAS GIVEN, BUT IT DID NOT INCLUDE THE NOTAM CONCERNING THE CLOSED PORTION OF RWY 17/35. AFTER BREAKING OUT OF THE OVERCAST, HE CANCELED HIS IFR FLT PLAN SO THAT ANOTHER PLT COULD BEGIN HIS DESCENT. THE PLT STATED THAT HE MADE A NIGHT APPROACH TO RWY 17 USING THE VASI AND APPROACH LIGHTS. DURING THE LANDING, THE ACFT TOUCHED DOWN ON THE CLOSED PORTION OF THE RWY IN APRX 18 INCHES OF SNOW. WHEN THE NOSE WAS LOWERED, THE NOSE GEAR FAILED, BUT THE DAMAGE WAS CONSIDERED TO BE MINOR.