AFTER LNDG IN REDUCED VISIBILITY; LTT TAXIED OFF RWY WHEN FLC COULDN'T FIND TAXI STRIP. RWY EXCURSION.

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I WAS THE PF ON FLT SCHEDULED PAX SVC FROM TORONTO INTL TO SYRACUSE; NY; IN ACFT; A TURBOPROP COMMUTER. AFTER STANDARD BEFORE LNDG AND APCH BRIEFING; WE MADE A NORMAL ILS APCH TO RWY 28 IN SYRACUSE. ATIS WX RPTED AT XA41Z WAS MINUS X 11 OVCST 1/2 SF SURFACE VISIBILITY 1/4 VARIABLE 3/4 (WIND 290 DEGS AT 17 KTS GUSTING 32 KTS). ON OUR APCH; CTLR ADVISED CURRENT VISIBILITY WAS 1/2 MI THE MINIMUMS FOR APCH PROC USED. RWY ENVIRONMENT WAS IN SIGHT AT 1000 FT AGL. WE CONTINUED FOR A NORMAL LNDG; BUT DUE TO BLOWING SNOW OBSCURING VISIBILITY; WE WERE ONLY ABLE TO SEE APPROX 2 RWY LIGHTS AHEAD OF US; ALL RWY MARKINGS WERE COVERED WITH SNOW AND ICE. WE DECELERATED TO A TAXI SPD OF ABOUT 5 MPH AND BEGAN SHALLOW TURN TOWARDS BLUE TAXI LIGHTS THAT WERE DIMLY VISIBLE. WHILE HDG TOWARDS SPACE BTWN LIGHTS WE SAW EDGE OF RWY. I APPLIED BRAKES; BUT COULD NOT STOP DUE TO ICE PATCH. NOSEWHEEL SKIDDED A COUPLE OF FT OFF OF RWY INTO A SNOW BANK. PAX WERE DEPLANED AND BUSSED TO THE TERMINAL. PLANE WAS THEN SUCCESSFULLY EXTRICATED FROM SNOW BANK USING COMPANY TUG. ACFT THEN TAXIED TO TERMINAL RAMP. ON INSPECTION; NOSEWHEEL WAS FOUND TO BE FLAT. NO OTHER DAMAGE TO ACFT INCURRED. THERE WERE NO INJURIES TO PAX OR CREW. THE CAUSES OF THIS INCIDENT WERE EXTREMELY POOR VISIBILITY AND POOR BRAKING DUE TO WX CONDITIONS AT THE TIME. IN MY OPINION THERE WAS NO ACTION WE COULD HAVE TAKEN TO AVOID SIT.