ACFT ATTEMPTING TO TURN FOR TAXI BACK AFTER LNDG ON SNOW COVERED RWY HAS NOSEWHEEL LEAVE RWY.

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APCHING ROC; ATIS RPTED WX AS 2300 FT OVCST; 1/2 MI VISIBILITY WITH SNOW AND FOG. WINDS 300/7. FIELD CONDITIONS RPTED TO BE RWY 22 BROOMED FULL WIDTH AND LENGTH; COVERING OF HARD PACK SNOW AND ICE; SCATTERED PATCHES OF LIGHT POWDER; SNOW DEPTH UP TO 1/2 INCH IN DEPTH; BRAKING ACTION FAIR TO POOR. ON FINAL APCH; TWR RPTED WINDS ESTIMATED 300/13G20. RWY BRAKING ACTION RPTED AS POOR BY AN MLG. IT WAS FO'S LEG. HE FLEW A NORMAL APCH AND LNDG. MEDIUM AUTO BRAKES WERE USED. THE FO BROUGHT THE ACFT TO A COMPLETE STOP ON THE CENTERLINE WITH ABOUT 2500 FT REMAINING. WE WERE ADVISED BY THE TWR THAT ALL TAXIWAYS WERE CLOSED EXCEPT FOR THE ONE AT THE ARR END OF RWY 22; WHICH LED TO THE RAMP. THE TWR INSTRUCTED US TO MAKE A 180 DEG TURN AND BACK TAXI TO THE RAMP. THE RWY WAS PLOWED APPROX 60 FT EITHER SIDE OF THE CTRLINE AND WAS COVERED WITH A LIGHT LAYER OF SNOW. BRAKING IN THAT AREA WAS POOR. THE LAST 15 FT ON EACH SIDE WAS NOT PLOWED AND THE SNOW WAS MUCH DEEPER THERE. I TOOK CTL OF THE ACFT AND SLOWLY TAXIED TO THE FAR R SIDE OF THE RWY. FROM THAT POINT; I BEGAN A HARD L TURN. ALL WAS NORMAL UNTIL HALFWAY THROUGH THE TURN APPROX 90 DEG TO THE RWY. AT THAT POINT; I JUDGED THE ACFT WAS MOVING TOO SLOWLY TO COMPLETE THE TURN SO I ADVANCED THE PWR SLIGHTLY ON THE OUTBOARD R ENG TO KEEP THE ACFT MOVING. THE TURN CONTINUED NORMALLY UNTIL ABOUT 120 DEG OF THE 180 DEG TURN HAD BEEN COMPLETED. THEN; WITH THE NOSEWHEEL IN THE CLUTTERED AREA OF THE RWY; STEERING CTL WAS LOST. BEFORE I WAS ABLE TO STOP THE ACFT; THE NOSEWHEEL LEFT THE PLOWED SECTION OF THE RWY AND THE ACFT CAME TO A STOP; STUCK WHERE I LATER FOUND WAS OFF THE RWY. CONTRIBUTING FACTORS: POOR BRAKING ON CTRLINE TO NIL AT EDGE UNDER SNOW; XWIND BEHIND AS FINISHING TURN; SLOPE OF RWY FROM CROWN AS COMPLETED TURN; INEXPERIENCE OF PLT IN JUDGING HOW MUCH SPD NEEDED TO COMPLETE TURN ON A CLUTTERED RWY AND FAILURE OF ARPT TO CLOSE ARPT. CORRECTIVE ACTION: PLOW TAXIWAY SO ACFT CAN RETURN TO RWY FOR BACK TAXI. MAKE TURN AT TAXIWAY INTXN.