THE TWR WAS CLOSED AT DBQ; AND AN ACR FLC EXECUTED A MISSED APCH UPON LEARNING THAT A SNOW PLOW WAS ON THE RWY.

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AFTER GETTING DEICED; WE WERE ON OUR WAY TO DBQ. AT APPROX 15 MINS AWAY FROM DBQ ARPT; WE LEARNED THAT THEIR TWR WAS CLOSED FOR THE EVENING; AND ADVISED BY ZAU THAT POSSIBLE SNOW PLOWING WAS IN PROGRESS. AS WE RECEIVED RADAR VECTORS FOR THE ILS; WE CALLED DBQ FOR A 'TFC CHK.' THERE WAS NO TFC; EXCEPT FOR SNOW PLOWS ON THE RWY. WE TRIED UNSUCCESSFULLY TO COMMUNICATE WITH THE SNOW PLOWS. THEN; WE REALIZED WE HAD TUNED TO AN INAPPROPRIATE FREQ FOR CTAF. AFTER TUNING TO THE DBQ CTAF; WE LEARNED THE SNOW PLOWS WERE ACTIVELY CLEANING THE ACTIVE RWY WHILE WE WERE ON A 2 MI INST APCH. I IMMEDIATELY INITIATED A MISSED APCH AND WE WERE VECTORED AROUND FOR ANOTHER ILS. AFTER GUARANTEEING THE SNOW PLOWS WERE CLR OF THE RWY; WE LANDED AND TAXIED TO OUR GATE WITHOUT INCIDENT. I BELIEVE THAT A LENGTHY SCHEDULE AFTER MINIMAL REST; CREATED A POTENTIALLY DISASTROUS SIT. THE COMBINATION OF POOR WX; REQUIRING PRECISE AERO AND NAV SKILLS; COUPLED WITH 14+ HRS OF DUTY; OVERSHADOWED OUR ABILITY TO COMMUNICATE PROPERLY.