BE1900 FLT CREW HAS SMOKE IN THE COCKPIT DURING CRUISE; DSCNT.

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WE WERE DSNDING OUT OF FL200 FOR 15000 FT. GIVEN BY ATC; CONDITIONS WERE MOSTLY IMC. ALL ANTI-ICE EQUIP ON. I BEGAN TO SMELL SOMETHING BURNING AND NOTIFIED CAPT. CAPT AGREED. APPROX 7 SECONDS LATER; PASSING THROUGH APPROX 16000 FT; SMOKE STARTED COMING THROUGH CAPT'S CTL COLUMN. CAPT IMMEDIATELY TURNED OFF ALL ANTI-ICE EQUIP EXCEPT ENG ANTI-ICE AND PUT ON HIS OXYGEN MASK. I CONTINUED TO FLY THE ACFT. THE SMOKE BEGAN TO IMMEDIATELY DISSIPATE. CAPT NOTIFIED ATC; ASKED FOR A LOWER ALT AND DIRECT ZZZ1 WITHOUT DELAY. WE RECEIVED A HDG FOR DIRECT ZZZ1 AND 10000 FT FOR THE ALT. ATC DECLARED AN EMER. NO FURTHER INDICATIONS OF SMOKE OR FIRE WERE PRESENT. IT SEEMS THE CAPT'S IMMEDIATE REACTION TO SHUT OFF ANTI-ICE EQUIP ALLEVIATED FURTHER DAMAGE TO THE ACFT. WE WERE VMC PASSING THROUGH APPROX 15500 FT. WE RAN ALL PERTINENT CHKLISTS; DISCUSSED LNDG OPTIONS INCLUDING SPD FOR FLAPS 0 DEG LNDG IF SMOKE RETURNED. IN ZZZ1 WE LANDED FLAPS 0 DEGS; TAXIED AND PARKED WITHOUT FURTHER INCIDENT. SUPPLEMENTAL INFO FROM ACN 686535: THE FO CALLED FOR THE CHKLIST AND HE WENT THROUGH THEM ALL. HE DISCUSSED ITEMS THAT WERE RELEVANT TO OUR SITUATION AND OPTIONS WE HAD IF THE PROB RETURNED; INCLUDING OTHER POSSIBLE LNDG SITES. SEVERAL WIRES ON THE CAPT'S SIDE WERE BURNED AND MELTED; INCLUDING ONE WIRE THAT WENT ACROSS TO THE FO'S SIDE. THE PROB WAS TRACED TO A SHORT IN THE WINDSHIELD ICE WIRING.