TXWY EXCURSION AFTER LOSS OF ACFT CTL.

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ARRIVED AT CMH JUST AS RWY 28L OPENED AFTER PLOWING. ATIS WAS RPTED AS 27 BROKEN 45 OVCST 7ZR -30 DEGS 190 /15 29.81; BRAKING RPT EQUALED GOOD. NO COMMENTS MADE REGARDING TXWYS OR RWY EXITS. LANDED ON RWY 28L AND ROLLOUT BRAKING WAS GOOD. SLOWED TO TAXI SPD TO EXIT RWY 28L AT C4. AS WE EXITED THE PLOWED PORTION OF RWY 28L ONTO C4; APPARENTLY TAXIED ONTO AREA OF CLR ICE. LOST ALL CTL OF NOSE STEERING AND BRAKING. ACFT SLOWLY SLID OFF L SIDE OF TXWY C4. L MAIN MOUNT AND POSSIBLY NOSEWHEEL OFF TXWY ONTO FROZEN GND. LET ACFT CONTINUE TO ROLL BY DISCONTINUING ATTEMPTED BRAKING AND IT ROLLED BACK ONTO INTXN OF C4 AND TXWY C; WHERE I MANAGED TO STOP ACFT WITH BRAKES ON CTRLINE OF TXWY C. NOTIFIED TWR AND GND THAT WE HAD SLID OFF TXWY AND REQUESTED OUR MAINT TO COME CHK ACFT PRIOR TO CONTINUED TAXI. HAD CRASH CREW CHK TO SEE IF ANY TXWY LIGHTS OR OTHER OBJECTS HAD BEEN IMPACTED. MAINT CAME OUT AND CHKED ACFT; SAW NO PROB; AND WE TAXIED TO GATE. HAD ARPT MGR RECHK TXWY C4 AND HE STATED TRACKS INDICATED ACFT DID NOT ROLL OVER ANY TAXI LIGHTS OR BREAK THROUGH GND CRUST. I BELIEVE I WAS MISLED BY GOOD BRAKING ON THE RWY AND APPARENTLY CLR EXIT. VISUALLY THE EXIT LOOKED IN AS GOOD CONDITION AS THE RWY. SHOULD HAVE BEEN MORE ALERT TO POSSIBILITY OF CLR ICE ON TXWY C4 AS RESULT OF PREVIOUS PLOWING OF RWY. IF TWR WAS AWARE OF CONDITION OF EXITS; WOULD HAVE BEEN VERY BENEFICIAL TO HAVE HAD A WARNING/ALERT FROM THEM. THIS HAS SERVED TO RENEW MY VIGILANCE ON CONTAMINATED RWYS AND TXWYS. AFTER 25 YRS OF OPERATING EXPERIENCE IN ALL TYPES OF WX CONDITIONS; THIS INCIDENT PROVED AGAIN HOW QUICKLY ICING CONDITIONS CAN CHANGE AND AFFECT SAFE OPS.