RWY INCURSION BY ACR FRT HAULER IN A NIGHT OP.

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ON JAN/XX/94 WE FLEW INTO GREEN STATE ARPT; PROVIDENCE; RI. WHEN WE ARRIVED IN PVD THAT MORNING THE ONLY RWY AVAILABLE WAS 16/34 BECAUSE A HVY SNOW STORM CLOSED RWYS 5L/23R & 5R/23L AND MOST OF THE TXWYS. WE DIDN'T EXPERIENCE OUR PROB UNTIL THAT EVENING WHEN WE BEGAN TO TAXI OUT TO RWY 34 FOR TKOF. THE TXWYS WERE STILL COVERED WITH SNOW AND ICE WHICH MADE TAXIING THE ACFT CHALLENGING. MY FO WAS BRAND NEW IN THE ACFT; HAVING ONLY CHKED OUT A FEW MONTHS EARLIER. THE SO HAD FLOWN PVD SEVERAL TIMES THAT MONTH AND I HAD NOT BEEN TO PVD IN OVER A YR. EACH TIME I HAD FLOWN INTO AND OUT OF PVD WE USED RWY 23L OR 5R BECAUSE IT IS LONGER AND MORE CONVENIENT TO OUR CARGO RAMP. WE RECEIVED CLRNC TO TAXI VIA 'A' TO 'B' AND HOLD SHORT OF RWY 34. AS WE APCHED OUR HOLDING POINT THE TWR CLRED AN ACFT TO LAND ON RWY 34 AND THEN CLRED US TO TAXI TO RWY 34 VIA TXWY K WITH A COMMENT 'NO DELAY; ACFT 2 MI FINAL.' THE POS WE WERE AT HAS TXWY B; H; G; AND J CONVERGING AS WELL AS RWY 34 AND 23L. AS I BEGAN TO CROSS RWY 34 FOR TXWY K I COULD NOT DISCERN TXWY K BECAUSE FOR ONE THING; WE HAD TO CROSS RWY 34 AND THEN TAXI DOWN RWY 23L TO TXWY K AND SECONDLY; THE TXWY MARKINGS AND SIGNS FOR TXWY K WERE OBSCURED BY SNOW. I MISTAKENLY CONTINUED DOWN RWY 34; MISSED THE TURNOFF TO RWY 23L AND THE SUBSEQUENT TURNOFF TO TXWY K. AS IT TURNS OUT I COULD NOT EXIT RWY 34 ONCE I PASSED RWY 23L SINCE TXWY J IS RESTR TO ACFT 12500 LBS OR LESS. I WAS BLOCKING THE RWY FOR THE LNDG TFC. PVD TWR DIRECTED THE ACFT ON SHORT FINAL TO GAR WHICH IT DID AND THEN DIRECTED US TO TAXI DOWN RWY 34 FOR TKOF ON 34. WHEN I ASKED THE FO IF THE TAXI CLRNC DIRECTED US TO CONTINUE ACROSS RWY 23L HE SAID NO; TURN L. THAT PUT US IN THE POS WE FOUND OURSELVES BUT I CANNOT FAULT THE FO. IN HINDSIGHT; I SHOULD HAVE TOLD THE TWR CTLR THAT WE WOULD HOLD SHORT FOR THE LNDG TFC IN ORDER TO BE ASSURED OF THE PROPER TAXI RTE. THAT WOULD NOT ONLY ALLOW ME TO FEEL COMFORTABLE WITH THE TAXI RTE BUT ALSO NOT HAVE TO EXPEDITE MY TAXIING ON A SNOW AND ICE COVERED TXWY. SEVERAL FACTORS INFLUENCED THIS SIT WHICH I AM SURE YOU CAN DISCERN FROM THE ABOVE NARRATIVE. SUFFICE TO SAY THAT GIVEN THE CREW COMPOSITION AND METEOROLOGICAL CONDITIONS AT THE TIME MY BEST ALTERNATIVE WOULD HAVE BEEN TO SLOW DOWN THE SEQUENCE OF EVENTS AND ASSURE MYSELF A PROPER TAXI RTE.