B737-300 CREW STARTED TO EXIT THE RWY ON A CLOSED TXWY. ANOTHER ACR HAD TO DO A GAR.

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CAPT (SELF) FLYING; FO MONITORING PLT. BRIEFED ARR/APCH/INTENDED RWY TURNOFF POINT/TAXI RTE TO GATE; PRIOR TO TOP OF DSCNT. FO LEFT FREQ ON DSCNT TO OBTAIN ATIS (B737-300) AND NOTIFY COMPANY OF ARR TIME/SPECIALS AND TO GET GATE ASSIGNMENT. FO RETURNED TO FREQ WITH ATIS SLIP WITH ARPT INFO AND GATE ASSIGNMENT. DISCUSSED ARR WX AND GATE INFO. WX 3800 FT BROKEN AND VISIBILITY 10+ MI. INITIATED ILS RWY 29 APCH AND TRANSITIONED TO VISUAL APCH AND LNDG. INITIATED TURNOFF AT TXWY V. AS ACFT WAS ENTERING TXWY V; TWR ADVISED THAT TXWY V WAS CLOSED AS PER ATIS. SMALL RED CONES; APPROX 1 FT HIGH; BLOCKING ACCESS TO PARALLEL TXWY W FROM HOLD SHORT LINE COULD BE SEEN AS WE BEGAN EXITING RWY/ENTERING THE TXWY ABOUT 100 FT AHEAD (COULD NOT BE SEEN WHILE ON RWY). TWR INSTRUCTED US TO CONTINUE AHEAD THROUGH BLOCKED TXWY AS SHE CLRED AN ACR Y TO LAND AND ADVISED THEM THAT TXWY V WAS CLOSED. I DECIDED NOT TO GO THROUGH BARRIER; TURNED ACFT SO AS TO CONTINUE DOWN RWY AND ADVISED TWR WE WOULD CONTINUE TO NEXT TXWY. TWR ADVISED ACR Y THAT AN ACFT (US) WAS STILL ON RWY AND TO BE PREPARED FOR POSSIBLE GAR. AS WE WERE EXITING RWY ONTO TXWY Y; TWR ADVISED ACR Y TO GAR; US TO CONTACT GND. WE CONTACTED GND CLR OF RWY AND TAXIED TO GATE. ON TAXI IN; I QUERIED FO IF HE HAD HEARD ON ATIS FREQ THAT TXWY V WAS CLOSED. HE RESPONDED THAT THERE WERE MANY TXWYS CLOSED AND THAT THEY WERE TOO NUMEROUS TO WRITE DOWN ON THE ATIS SLIP. EVENT COULD HAVE BEEN AVOIDED IF COMPLETE ATIS WRITE-DOWN HAD BEEN COMPLETED. HOWEVER; THIS WOULD RESULT IN A SINGLE PLT OP FOR AN EXTENDED PERIOD OF TIME DURING A HIGH WORKLOAD ENVIRONMENT (TRANSITION DURING DSCNT FROM CTR FREQS TO SEVERAL APCH FREQS WHILE TRYING TO COMPLY WITH XING RESTRS. TWR SHOULD STATE TO 'ALL' LNDG ACFT; ANY RWY EXITING TXWYS WHICH ARE CLOSED; REGARDLESS OF ANY ATIS CONTENT. MARKER CONES OR BARRIERS SHOULD BE PLACED AT THE RWY EDGES SO AS TO BE COMPLETELY VISIBLE TO ACFT FROM RWY.