CL65 CAPT EXPERIENCED A LACK OF NOSEWHEEL STEERING CTL WHEN ATTEMPTING TO TURN AND TAXI OFF THE RWY AFTER LNDG ON A SNOW COVERED ICY RWY.

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ACR X FLT WAS CLRED FOR THE RWY 1 ILS APCH. VISIBILITY WAS RPTED 1/2 MI; BRAKING ACTION FAIR. VISIBILITY 1/2 MI DUE TO SNOW SHOWER AT ARPT (CAK). LANDED ON RWY; BUT FOUND ONLY L SIDE OF RWY WAS PLOWED. PROBABLY WAS A GOOD INCH OR BETTER OF SNOW ON R SIDE OF RWY; THE WHOLE LENGTH. BRAKING ACTION WAS VERY POOR AND STOPPED ACFT COMPLETELY ON RWY. WHEN I TRIED TO TURN OFF RWY; ACFT STEERING WOULD NOT RESPOND DUE TO RWY CONDITIONS. ACFT WOULD JUST SLIDE TOWARDS THE SIDE OF RWY. NOTIFIED TWR IMMEDIATELY THAT WE WERE UNABLE TO CLR RWY; IN WHICH HE RESPONDED 'IT'S OK.' ALL OTHER ACFT INBOUND HAVE GONE TO THEIR ALTERNATES; AND THEY WERE SHUTTING DOWN THE ARPT UNTIL THEY COULD GET ONE OF THEIR RWYS CLEANED OFF. WE HAD COMPANY COME OUT AND TOW US IN WITH A TUG. NO DAMAGE TO ACFT. I BELIEVE A BETTER WAY OF DETERMINING BRAKING CONDITIONS; OTHER THAN A CAR TRAVELING DOWN THE RWY; SHOULD BE USED. I ALSO FEEL TWR SHOULD HAVE NOTIFIED ME THAT ONLY L HALF OF RWY WAS PLOWED. THIS HAD THE POTENTIAL OF BEING A VERY SERIOUS PROB.