AN ACR CREW REPORTS BEING UNABLE TO SEE TXWY EDGES AND TAXIING THE NOSE WHEEL OFF A TXWY COVERED IN SNOW. ACFT SHOULD HAVE BEEN TOWED TO THE GATE.

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DEPARTING FOR ZZZ; WE RECEIVED DEP WX INDICATING THAT ZZZ HAD 1/2 MI VISIBILITY; SNOW; AND GUSTY WIND CONDITIONS. ENRTE; THE ATIS INDICATED 3/4 MI VISIBILITY; 6 MI BROKEN; LIGHT SNOW; AND WINDS OF 320 DEGS AT 10 KTS GUSTING TO 16 KTS. I ELECTED TO FLY THE ILS CAT II APCH DUE TO THE GUSTY WINDS; LOW VISIBILITY; AND SNOW CONDITIONS AT ZZZ. WE DID OUR LNDG DATA WITH WET/FAIR AND HAD SUFFICIENT STOPPING MARGIN FOR MINIMUM BRAKING. WE BRIEFED THE APCH AS A CAPT FLOWN CAT II APCH AND WE BRIEFED THE TAXI RTE TO GATE AS EXITING THE RWY ON EITHER HIGH SPD TXWY XX OR XY N ON XZ; A SHARP R TURN ONTO TXWY XW; THEN A SLIGHT L TO THE GATE. IN DSCNT WE RECEIVED UPDATED WX OF WINDS 320 DEGS AT 11 KTS; 1/4 MI VISIBILITY; HVY SNOW; VV004; AND BRAKING ACTION FAIR. WE ASKED FOR THE RVR AND RECEIVE RWY XX; RVR: TOUCHDOWN 3000 FT; MIDPOINT 3000 FT; ROLLOUT 2800 FT. WE RECEIVED VECTORS TO THE ILS XXL; FLEW THE ILS XXL CAT II APCH; AND MADE AN UNEVENTFUL LNDG. WE EXITED THE RWY AT HIGH SPD TXWY XX AND TURNED NBOUND ON TXWY XZ. HVY SNOW WAS FALLING AND HAD EVIDENTLY BEEN ACCUMULATING FOR A WHILE. ALL TXWY MARKINGS AND CTRLINE LIGHTS WERE COVERED WITH SNOW AND THERE WERE NO VISIBLE ACFT TRACKS FROM PRECEDING ACFT. THE ONLY VISIBLE TXWY INDICATIONS WERE THE RAISED TXWY EDGE LIGHTS ON THE SIDES OF THE TXWYS AND WE USED THESE LIGHTS AS REF TO TAXI. ALSO; FALLING SNOW AND WIND BLOWN SNOW MADE THE VISIBILITY A CHALLENGE EVEN WITH THE LNDG LIGHTS ON. WE WERE INSTRUCTED BY GND CTL TO TAXI XZ; XW; TO THE GATE. WE BOTH VERIFIED THE RTE AGAINST OUR ARPT DIAGRAM. THE RTE MATCHED OUR BRIEFED TAXI PLAN AND WE SLOWLY PROCEEDED NBOUND ON TXWY XZ. WE MONITORED OUR PROGRESS AS WE PROCEEDED NBOUND AND NOTED XING RWY XX THAT IT WAS COMPLETELY COVERED WITH SNOW. AFTER XING XX; WE BEGAN LOOKING FOR THE APPROX 120 DEG R TURN ONTO TXWY XW TO OUR R. THE SNOW WAS VERY DEEP ON THE TXWY AT THIS POINT AND WE SAW AHEAD AND TO OUR R WHAT APPEARED TO BE THE RAISED LIGHTS OF TXWY XW ON THE R AND AS WE GOT CLOSER WE SAW WHAT APPEARED TO BE TAXI TRACKS ON THE TXWY TOWARD THE RAMP. WE SLOW THE ACFT TO LESS THAN 5 KTS AND AGREED THAT THIS WAS TXWY XW TO OUR R. I BEGAN THE R TURN AND 1/2 WAY THROUGH THE TURN; GND CALLED AND SAID THAT WE'D MISSED OUR TURN AND TO CONTINUE N FOR A 180 DEG TURN. THE FO ANSWERED THAT WE WERE IN THE TURN. CONFUSED BY THE RADIO CALL; I ATTEMPTED TO BRAKE THE ACFT TO A STOP. THE ACFT SLID ON THE SNOW WITH POOR BRAKING. I CTRED THE NOSEWHEEL AND AS WE SLID TO A STOP WE FELT THE NOSEWHEEL DROP. ASSUMING THAT THE NOSEWHEEL WAS OFF THE TXWY; WE INFORMED GND CTL AND COMPANY. WE REQUESTED ASSISTANCE FROM OPS; WE STARTED THE APU; AND SHUT DOWN THE ENGS. WE COORD WITH COMPANY THROUGH ZZZ OPS AND DISPATCH FOR ASSISTANCE TO GET TRANSPORTATION FOR OUR PAX AND EQUIP FOR GETTING THE ACFT UNSTUCK AND TO THE GATE. I INFORMED THE PAX THAT WE WERE STUCK AND WE WERE MAKING ARRANGEMENTS TO GET THEM TO THE GATE. OPS BROUGHT OUT A SET OF AIR STAIRS AND WE DEPLANED THE PAX THROUGH THE REAR ENTRY AND TRANSPORTED THEM TO THE TERMINAL VIA BUS. WE THEN WORKED WITH A MECH TO EVALUATE THE ACFT AND SEE WHAT WE COULD DO TO GET THE NOSEWHEEL BACK ON THE TXWY. HE EVALUATED THE ACFT AND SAID THE ACFT WAS UNDAMAGED. HE THEN PROCEEDED TO DIG OUT THE SNOW AROUND THE NOSEWHEEL SO WE COULD PULL THE ACFT OUT ONCE EQUIP ARRIVED. AFTER 6 HRS OF WORK INVOLVING SNOWPLOWS; A LARGE TOW TRUCK; AND ONE OF OUR TUGS; WE RODE THE BRAKES AND THE ACFT WAS TOWED TO THE RAMP BY OPS PERSONNEL. AFTER THE HVY SNOW STOPPED; WE BEGAN TO SEE OUR SURROUNDINGS MORE CLEARLY. WE REALIZED THAT TXWY XW HAD BEEN COVERED WITH HVY SNOW AS WE CROSSED IT AND AS A FURTHER COMPLICATION; 4 OF TXWY XW LIGHTS; ON THE N SIDE OF TXWY XW WERE IT INTERSECTS WITH TXWY XU; WERE NOT LIGHT AT ALL -- BUT RATHER UNLIT BLUE POLES. THIS COMBINATION OF NO EDGE LIGHTS ON THE N SIDE OF TXWY XW AND HVY SNOW MADE TXWY XW APPEAR NOT TO BE A TXWY IN THE HVY SNOW CONDITIONS. WHAT WE PERCEIVED TO BE THE TXWY XW LIGHTS WERE REALLY CARGO RAMP EDGE LIGHTS ON THE R (N) SIDE AND THE FEW REMAINING LIT TXWY XW LIGHTS ON THE L (S) SIDE. THE PERCEIVED ACFT TAXI TRACKS WERE TUFTS OF GRASS IN THE SNOW IN A RAISED AREA OF EARTH RUNNING PARALLEL TO TXWY XW. WE WERE FOOLED BY FALSE CUES THAT SHOWED US BOTH WHAT WE EXPECTED TO SEE. THE AMOUNT OF SNOW AT ZZZ MADE CORRECTLY IDENTING TXWY XW VERY DIFFICULT WITH AN ABSENCE OF RAISED LIGHTS ON THE N SIDE OF THE TXWY. IN HINDSIGHT; I WOULD COMPLETELY STOP THE ACFT AND ASK FOR THE ASSISTANCE OF A FOLLOW-ME OR A TUG TO THE GATE. SUPPLEMENTAL INFO FROM ACN 777494: I BEGAN DAY 3 OF A 4-DAY RESERVE BLOCK IN OUR DEP CITY. RERTES THE PRIOR DAY LED TO A 16 HR 32 MIN DUTY DAY WITH 9 HR 3 MIN REST. DESPITE THE LONG DAY AND SHORT REST PERIOD; I FELT ADEQUATELY RESTED FOR THE DAY AHEAD WHICH WAS TO BE 2 LEGS AND 2 DEADHEADS.