DURING ARRIVAL FROM VFR-ON-TOP, THE PLT WAS GIVEN RADAR VECTORS FOR THE NDB APCH. THE PLT STATED THAT HE WAS IN THE CLOUDS DURING THE APCH FOR ONLY ABOUT 5 TO 8 MIN. HE REPORTED THAT APRX 1/2 MI OUT ON FINAL APCH, THE NOSE BECAME PROGRESSIVELY HEAVY AND THE AIRSPEED GAGE WAS INDICATING 90 KTS. A GO-AROUND WAS STARTED. REPORTEDLY, THE AIRSPEED INCREASED TO 92 KTS, BUT THE NOSE PITCHED FURTHER DOWN. SUBSEQUENTLY, THE ACFT TOUCHED DOWN HARD, NOSEWHEEL FIRST, BOUNCED & STRUCK THE RWY. THE NOSEWHEEL COLLAPSED DURING THE LANDING & THE ACFT CAME TO REST JUST OFF THE RWY. REPORTEDLY, PRX 1/8 INCH OF ICE ACCUMULATION WAS FOUND ON THE LEADING EDGES OF THE WINGS. AN INVESTIGATION REVEALED NO FLT CONTROL PROBLEMS. THE PLT BELIEVED THAT ICE HAD ACCUMULATED ON THE PITOT TUBE. HE STATED THAT THE PITOT HEAD WAS SLOW TO HEAT AFTER THE ACCIDENT. ACCORDING TO HIM, THE ACFT ACTED LIKE IT WAS FLYING AT ONLY 75 TO 80 KTS WHEN IT TOUCHED DOWN HARD.