COMMUTER TAXIING IN SNOW ENTERS ACTIVE RWY DUE TO CONFUSING SIGNAGE.

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TAXIED ACFT ONTO RWY. IT WAS THE ACTIVE BUT BEING PLOWED AND BRUSHED AT TIME OF INCURSION. CONTRIBUTING FACTORS: WX; SNOW HAD FALLEN ON RAMP AND BLOWN/DRIFTING ONTO SIGNS TO SOME EXTENT. GND CTL WAS TALKING TO SNOW PLOWS ON THE RWY. GND THEN ASKED US IF WE WERE READY TO GO BEFORE WE WERE IN ANY POS TO TAKE OFF. THERE WAS NO TFC CONFLICT WITH THIS. HUMAN FACTORS: LATE NIGHT AND FLYING LAST 2 DAYS DEALING WITH STRONG LOW PRESSURE SYS; TIRED DUE TO ROUGH RIDES; NUMEROUS APCHS TO MINIMUMS WITH STRONG XWINDS AND TURB WITH BLOWING SNOW. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES HE HAS NOT BEEN BACK TO CAK SINCE THIS INCIDENT SO CANNOT REALLY TELL WHERE THE SIGNS GET CONFUSING. ONE HAS TO CROSS RWY 32/14 GETTING TO RWY 1 AND THE NORMAL PROC IS TO TAXI ON TXWY A. SEEING THE SIGN PLACED PRIOR TO RWY 1/19 BUT INDICATING RWY 32/14 ASSURED THEM THEY WERE XING THE NON ACTIVE TXWY. RPTR FEELS STRONGLY THAT THE SIGN GIVES MISINFO AND DOES NOT INDICATE THE CORRECT RWY. THEY HAD TO BACK TAXI FOR TKOF. OF COURSE THE SNOW CONDITIONS ADDED TO THE PROBS ALONG WITH CTLR QUERYING IF THEY WANTED TO TAKE OFF RIGHT AWAY OR WAIT UNTIL SNOW REMOVAL WAS COMPLETED.