A CPR MDT TAXIED OFF OF A TXWY IN UNPLOWED SNOW.

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AFTER AN IFR LNDG AT DTW ON RWY 3L; TWR ASKED US TO 'MAKE THE NEXT AVAILABLE TXWY.' THE RWY WAS COVERED WITH PACKED SNOW AND ICE; SO WE CAME TO A NEAR STOP. THE ARPT HAD RECEIVED APPROX 8 INCHES OF SNOW AND NONE OF THE TXWYS HAD BEEN PLOWED. THIS INFO WAS RELAYED TO THE OTHER PLT VIA ATIS OR COMPANY OPS. TRYING TO ACCOMMODATE TWR; KNOWING ANOTHER ACFT WOULD SOON BE LNDG; WE ATTEMPTED TO EXIT THE RWY AT A REVERSE HIGHSPD TXWY THAT HAD NOT BEEN USED SINCE THE SNOW BEGAN. SEVERAL TXWYS CONVERGED HERE; PRODUCING A MAZE OF BLUE TAXI LIGHTS. NOT BEING SURE WHERE THE TXWY WAS; I STARTED BRAKING AND TOLD THE CAPT (IN THE R SEAT) OF MY MISGIVINGS. HIS CONCERN WAS BOGGING DOWN IN THE DEEP SNOW AND HE REACHED OVER AND PUSHED THE THROTTLES UP. ALTHOUGH NOT APPARENT FROM THE COCKPIT; WE DEPARTED THE TXWY ONTO FROZEN GND COVERED WITH DEEP SNOW AND BOGGED DOWN. THE RWY WAS CLOSED AND THE ACFT DIVERTED. IF I COULD DO IT OVER AGAIN; I WOULD EXIT THE RWY WHERE THE PREVIOUS ACFT WERE EXITING. AT LEAST THERE WOULD BE TRACKS TO FOLLOW. IF YOU CAN'T CLR THE TXWYS; MAYBE THE ARPT SHOULD BE CLOSED (NO INJURIES/DAMAGE).