A BE20 PLT EXPERIENCED DIFFICULTY MOVING THE ACFT'S ELEVATOR TRIM AFTER FLT IN ICING WITH THE AUTOPLT ON.

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I WAS FLYING AN EMPTY LEG REPOSITION SINGLE PLT IN A BE200. THE WX WAS IMC IN FREEZING TEMP; BUT THERE WAS NO STRUCTURAL ICE ON ACFT. AFTER LEVELING OFF AT CRUISE; I SET THE AUTOPLT AND BEGAN SETTING UP THE ILS 29 APCH. I WAS GIVEN A DSCNT CLRNC TO 2100 FT AND A HDG TO JOIN THE LOC. WHILE IN THE DSNDING TURN; THE AUTOPLT DISENGAGED AND THE ACFT PITCHED DOWN. WHEN I PULLED UP TO RECOVER; I COULD FEEL HVY RESISTANCE ON THE ELEVATOR CTL. I GRABBED THE MANUAL TRIM WHEEL TO TRY TO TRIM OFF THE PRESSURE; BUT THE WHEEL WAS FROZEN IN A NOSE DOWN TRIM CONFIGN. FIGHTING THE HVY NOSE DOWN ELEVATOR PRESSURE AND UNABLE TO MOVE THE TRIM WHEEL; I DECLARED AN EMER. AT THIS TIME I WAS BELOW MSA AND OFF COURSE SO I FOUGHT TO MAINTAIN ALT AND TURNED BACK TO TRY TO REJOIN THE LOC AND/OR FIND THE ARPT. ATC HELPED BY GIVING POS RPTS TO THE ARPT. THE LAST RPT SAID I WAS 1 1/2 MI FROM THE ARPT AND ARPT WAS AT MY 1 O'CLOCK POS. AT THIS TIME; I VISUALLY IDENTED THE ARPT AND LANDED WITHOUT INCIDENT. MAINT INSPECTED FLT CTLS AND TRIM AND FOUND NOTHING THAT WOULD CAUSE THE PROB. IT IS SUSPECTED THAT ICE FORMED SOMEWHERE ON THE TRIM MECHANISM; CAUSING IT TO FREEZE IN POS AT CRUISE.