DHC-8 FLT CREW HAS A RWY EXCURSION DURING INCLEMENT WX PRIOR TO TKOF.

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ON THE MORNING FLT WE STARTED OUR TAXI OUT TO RWY 23 IN SNOW AND LOW VISIBILITY (3/4 MI VISIBILITY AND LIGHT SNOW). CAPT HAD A TOUGH TIME SEEING THE TXWY DUE TO SNOW AND POORLY PLOWED TXWY. THE TXWY WAS ALSO PRETTY NARROW SO I WATCHED OUT MY SIDE WINDOW AT THE TAXI LIGHTS SO HE WOULDN'T HIT THEM. AS WE GOT NEAR THE END OF THE TXWY; I MADE A CALL TO REMOTE AND THEY SAID 'NO VISIBLE TFC.' THEN MADE A CALL TO TFC WHICH THERE WAS NO OTHER TFC BESIDE THE SNOW PLOW. AS WE STARTED ROUNDING THE CORNER OF TXWY A ONTO THE EXTENDED THRESHOLD OF RWY 23; CAPT CALLED FOR 'BELOW THE LINE' WHICH INVOLVES ME TURNING THE XPONDER ON; CTL CHK; HIGH LOW CHIME FOR THE FLT ATTENDANT; YAW DAMPER AND FLT DIRECTOR; AND BLEEDS OFF AND MIN. AS I WAS DOING MY CTL CHK WHICH INVOLVES ME LOOKING IN THE COCKPIT AT A GAUGE (PFLS); I NOTICED OUT OF THE CORNER OF MY EYE THE REILS LIGHTS GO BY. I LOOKED UP AND NOTICED THAT THE CAPT HAD TAXIED THE ACFT OFF THE EXTENDED THRESHOLD INTO THE DIRT WHICH WAS COVERED IN SNOW. I ADVISED THE CAPT THAT HE JUST TAXIED OFF OF THE EXTENDED THRESHOLD. WE PARKED THE PLANE THERE; CANCELED OUR IFR CLRNCS WITH ZZZ1 RADIO; AND NOTIFIED OUR COMPANY RIGHT AWAY OF THE EVENT IN THE CAPT'S DEFENSE HE THOUGHT THAT THE GRASS POPPING UP ABOVE THE SNOW WAS THE RWY IN THE DARK AND POOR VISIBILITY. SUPPLEMENTAL INFO FROM ACN 685793: WHEN WE GOT TO THE RWY THE PLOWING STOPPED. THERE WAS ALL SNOW AHEAD. SO I CONCENTRATED ON THE PATCHY SPOTS THAT WERE THERE WHEN WE LANDED. I WAS LOOKING AHEAD AND SAW SOME PATCHY SPOTS. THE FO WAS CONCENTRATING ON THE AILERON AND SPOILER GAUGE BECAUSE OF THE DEICING. HE THEN LOOKED UP AND SAID I WAS OFF THE RWY.