B737 EXPERIENCED GND CONFLICT AT GEG WHEN TURNING OFF RWY DURING VERY LIMITED VISIBILITY WITH CTLR UNSURE OF CONFLICTING ACFT LOCATION.

Narrative

OUR FLT WAS FROM DEN TO GEG. RECEIVED THE ATIS AND LOW CEILINGS AND FREEZING FOG WAS OCCURRING. IN THE NOTAMS OR REMARKS OF THE ATIS THE ARPT WAS CONDUCTING 'LOW VISIBILITY TAXI RTES.' CAPT AND FO BRIEFED THE SPECIAL CHART AND EXIT PLAN. WE WERE #2 FOR THE APCH BEHIND AN ACR Y. NORMAL; BUT VERY LOW APCH OCCURRED. UPON AUTO-LNDG IN SPOKANE; WA; ON RWY 3 DUE TO RVR OF 800/800/800 THE CAPT SLOWED THE ACFT AND STARTED TO EXIT AT HIGH SPD TURNOFF F. AS WE EXITED THE RWY; THE FO ASKED TWR WHERE THE ACR Y WAS. REPLY BY TWR; 'HE EXITED THE END;' BUT WE NEVER HEARD HIM SAY HE WAS 'CLR OF THE RWY' AS PER THE LOW VISIBILITY TAXI CHART; BUT TWR SAID HE WAS TAXIING TO THE TERMINAL OR GATE AND TO CONTACT GND. THE CAPT STOPPED IMMEDIATELY AND I ASKED GND WHERE THE ACR Y WAS. HE SAID 'YOU DON'T SEE HIM?' WE RESPONDED NO. JUST THEN; THE ACR Y CROSSED IN FRONT OF US. WE RPTED CLR OF THE RWY AND ALL COMPULSORY RPTING POINTS AND SPECIAL INSTRUCTIONS BY GND UNTIL WE REACHED THE GATE. TAXIING OUT FOR RETURN FLT; WE ASKED GND IF WE COULD DO AN ENG RUNUP ON TXWY A DUE TO THE FREEZING FOG AND THE ENGS OF THE B737. WE ASKED IF THERE WERE ANY OTHER ACFT IN THE AREA AS TO AVOID JETBLAST. GND CALLED 'ACR Z WHERE ARE YOU?' NO REPLY. GND AGAIN LOST THE WHEREABOUTS OF ANOTHER ACFT AND OTHER ACFT ARE NOT FOLLOWING THE LOW VISIBILITY TAXI CHART AND MANDATORY COMMUNICATING WITH GND AS TO THEIR WHEREABOUTS.