ACFT LANDS AND LNDG ROLL IS GREATER THAN RWY REMAINING.

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THE WINDS AT XA52Z WERE 360 DEGS 6 KTS. AT XB52Z WINDS WERE 360 DEGS 11 KTS. OUR LNDG WAS AT XB21Z; SO I BELIEVE THE WINDS WERE HIGHER THAN 6 KTS AS RPTED. IF THEY WERE I WOULD HAVE NOT LANDED ON THAT RWY. ALSO THE TWR WAS CLOSED. I BELIEVE THE TWR SHOULD BE OPEN FOR SCHEDULED ACR LNDGS. I WAS THE CAPT ON SEP/XX/95 ON XX FLT FROM DFW-FYV. UPON LNDG INBOUND TO FYV WITH A FULL LOAD OF PAX WE RECEIVED A WX RPT OF CLOUDS BROKEN 1000 FT OVCST 2 MI VISIBILITY LIGHT RAIN AND FOG; WINDS 360 DEGS 6 KTS WHEN CTR CLRED US FOR THE APCH. AFTER BREAKING OUT OF THE WX WHILE LNDG; WE ENCOUNTERED THE ANTI-SKID LIGHT CAUTION LIGHT COMING ON. THE ANTI-SKID WAS ON WHILE I WAS APPLYING BRAKES AND REVERSE THRUST BUT THE ACFT DID NOT SEEM TO SLOW DOWN AS IT SHOULD. I APPLIED MAX BRAKES AND MAX REVERSE THRUST; BUT THE ACFT STOPPED WITH THE NOSEWHEEL 1 1/2 FT PAST THE PAVEMENT. I ATTEMPTED TO REPOSITION THE ACFT AND THE R MAIN TIRE STUCK IN THE MUD. WE CALLED DISPATCH AND OPS TO BUS THE PAX BACK TO THE TERMINAL AND MAKE ARRANGEMENTS TO TOW THE ACFT OUT. APPROPRIATE LOGBOOK ENTRIES REGARDING THE ANTI-SKID WERE ENTERED IN THE ACFT LOGBOOK. SUPPLEMENTAL INFO FROM ACN 316155: LATER ON WHILE EXAMINING ACFT FROM THE OUTSIDE I FELT THE WIND AND BECAME SUSPICIOUS TO ITS STRENGTH. NEXT HOURLY OBSERVATION TAKEN AT XB52 LCL RPTED WINDS 360 DEGS 11 KTS. I BELIEVE THE COMBINATION OF THE TAILWIND AND ANTI-SKID CAUSED US TO OVERRUN THE 6006 FT RWY. HAD THE TWR BEEN OPEN AT THE TIME OF THE INCIDENT MAY HAVE PLAYED A CRUCIAL ROLE IN OUR DECISION MAKING PROCESS AS AN UP TO THE MIN WINDS WOULD HAVE BEEN AVAILABLE.