RWY CONDITION ICE SNOW -- ACR TRIED TWICE TO TAXI OUT AND TKOF AND SLIDES OFF OF THE RWY THE SECOND TIME.

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FLT LEFT THE GATE AT XA23 WITH THE FOLLOWING TAXI INSTRUCTION L ON TXWY B -- R ON TXWY V TO TXWY D FOR RWY 6R. WHEN MAKING A HALF R TURN AT TXWY D; THE NOSE GEAR SLID AND BRAKING ACTION WAS NIL. WE DIDN'T LEAVE THE TXWY BUT I WAS CONCERNED ABOUT POSSIBLY HITTING A TAXI LIGHT; WHICH WE LATER CONFIRMED WE HAD NOT. WE NOTIFIED TWR AND RETURNED TO THE GATE FOR MAINT INSPECTION. NO DAMAGE WAS FOUND; ACFT SIGNED OFF; RE-RELEASED AND OFF THE GATE AT XB23. WE RECEIVED THE SAME TAXI INSTRUCTIONS FOR RWY 6R. TXWY D HAD BEEN SANDED SINCE OUR PREVIOUS TAXI. WE WERE CLRED FOR TKOF FROM THE TXWY. I ENTERED THE RWY USING EXTREME CAUTION AND MOVING VERY SLOWLY; I BEGAN TO CTR THE NOSE GEAR AFTER XING THE CROWN OF THE RWY. WE CONTINUED STRAIGHT AHEAD AND FOUND WE HAD NO EFFECTIVE STEERING OR BRAKING ACTION. REVERSERS WERE ALSO INEFFECTIVE. WE LEFT THE RWY ON A 60 DEG ANGLE FROM THE RWY. I WAS NOT SURE HOW FAR OFF THE RWY WE WERE DUE TO THE SNOW AND ICE COVERING THE RWY. WE NOTIFIED THE TWR AND AIRLINE MAINT ARRIVED WITH A TOW TUG. I WENT TO THE CABIN AND TALKED TO THE PAX. THE TUG PUSHED THE ACFT BACK ON THE RWY. THE MAIN GEARS WERE STILL ON THE RWY. WE WERE THEN TOWED TO THE GATE ARRIVING AT XC41. ACFT WAS SIGNED OFF AND WE FERRIED IT TO DFW. MANY THANKS TO YYZ MAINT AND STAFF FOR THEIR PROFESSIONALISM -- TEAMWORK AND HELP.