AT APRX 0928 EST, THE PLT OBTAINED A FSS WX BRIEFING BY TELEPHONE. HE WAS BRIEFED ON CONDITIONS OF LOW CEILINGS, FOG, LIGHT RAIN, DRIZZLE, SNOW & BLOWING SNOW ALONG HIS ROUTE. HOWEVER, HE DID NOT ASK ABOUT ICING CONDITIONS & THE BRIEFING DID NOT INCLUDE A FLT PRECAUTION FOR ICING NOR A SIGMET (ISSUED AT 0820 EST) WHICH FORECASTED MODERATE TO SEVERE MIXED ICING. WHILE EN ROUTE, THE PLT MADE SEVERAL ATLITUDE CHANGES BY REQUEST. WHEN HE WAS QUERIED ABOUT A HEADING DEVIATION, HE REPLIED 'WE'RE HAVING A LITTLE PROBLEM.' THIS WAS THE LAST RADIO CONTACT. ATC RECEIVED NO RADIO CALLS CONCERNING ICING PROBLEMS OR AN EMERGENCY. WITNESSES NEAR THE CRASH SITE SAW THE ACFT COME OUT OF THE CLOUDS IN A NEAR VERTICAL DESCENT, ROTATING IN A NOSE DOWN ATTITUDE, THEN IMPACT & BURN. AIRFRAME ICE UP TO 1/2 INCH THICK WAS FOUND ON/NEAR PARTS THAT WERE NOT FIRE DAMAGED.