A B727 AFTER LNDG AND TAXIING ON THE RWY THE CREW WAS UNABLE TO FOLLOW TWR INSTRUCTIONS DUE TO SNOW AND DARKNESS.

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AFTER LNDG AT DTW; THE TWR CTLR SAID TO EXIT AT RWY 9 OR TXWY XXX (I CAN'T REMEMBER WHAT TXWY) AND INFORMED US THAT THERE WAS A ACFT ON 2 1/2 MI FINAL BEHIND US. IT WAS DARK AND HAD BEEN SNOWING AT DTW LONG ENOUGH TO LEAVE 6-8 INCHES OF SNOW. BRAKING ACTION ON THE RWY WAS FAIR AND SNOW AND SMALL SNOW DRIFTS WERE ON THE RWY WHEN WE LANDED. WE MISSED THE TXWY AS WE SLOWED THE ACFT ON THE ICY RWY. AT THIS TIME THE TWR CALLED AND SAID TFC IS NOW ON A 1 MI FINAL. THE CAPT TOLD THE FO TO TELL THE TWR WE WERE GOING TO EXIT AT RWY 9. AFTER THE FO WAS DONE WITH THE TWR XMISSION THE CAPT ASKED; 'IS THAT IT?' WE WERE EXITING OFF TO THE R AND THE CAPT WAS LOOKING DIRECTLY TO THE R OUT THE FO'S WINDOW. TO ME AND THE CAPT IT LOOKED LIKE THE FO WAS ALSO LOOKING TO THE R OUT THE FO'S WINDOW. TO ME AND THE CAPT IT LOOKED LIKE THE FO WAS ALSO LOOKING DIRECTLY TO THE R OUT OF HIS WINDOW WHEN HE REPLIED; 'YES THAT IS IT.' THE CAPT THEN SAID; 'ARE YOU SURE?' THE FO REPLIED; 'YES I AM SURE!' THERE WAS A FEELING OF URGENCY IN THE COCKPIT BECAUSE OF THE ACFT ON A 1 MI FINAL BEHIND US. THE CAPT THEN TURNED 90 DEGS TO THE R INTO THE SNOW/DIRT. TWR NOTICED WE HAD TURNED SHORT OF RWY 9 AND SENT THE ACFT BEHIND US AROUND. EVEN AFTER MAKING THE TURN IT WAS HARD TO TELL IF WE WERE IN THE WRONG AREA OR NOT; SNOW COVERED EVERYTHING TO AN EVEN DEPTH. THERE WERE NO SNOW BANKS OR ANY OTHER INDICATIONS OF WHERE THE EDGE OF THE RWY WAS. ALL OF THE TXWY LIGHTS WERE AT LEAST PARTIALLY COVERED WITH SNOW. AFTER TALKING OVER WHAT HAPPENED AS A CREW; IT TURNS OUT THE FO WAS NOT LOOKING OUT HIS WINDOW TO THE R AS THE CAPT AND I HAD ASSUMED. THE FO INFORMED US HE WAS LOOKING DOWN AT HIS CHART WHICH WAS CLIPPED TO THE WINDOW. WHEN HE LOOKED AT THE CHART; IT LOOKED LIKE HE WAS LOOKING OUT THE WINDOW. WHEN SOMETHING DOES NOT GO AS PLANNED; USUALLY EVERYBODY CAN TAKE SOME BLAME; AND OUR MISTAKE IS OBVIOUS. BUT WHAT MAY NOT BE SO OBVIOUS IS THAT THE SECOND CALL FROM TWR TELLING US THAT AN ACFT WAS ON A 1 MI FINAL WAS THE FINAL LINK IN THE CHAIN OF EVENTS LEADING TO US TAXIING OFF THE RWY IN THE WRONG SPOT.