ACFT TURNED SHORT OF RWY AND BRIEFLY LEFT THE PAVED SURFACE.

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IT HAD BEEN SNOWING ALL NIGHT AND EVERYTHING WAS COVERED WITH 6-8 INCHES ON THE GND. THE RWY HAD BEEN PLOWED BUT THERE WAS PLENTY OF COMPACTED SNOW TO MAKE THE BRAKING ACTION FAIR. WE LANDED NORMALLY; XFERRED CTL OF THE ACFT BTWN THE FO AND MYSELF IN AN ORDERLY MANNER; SLOWED THE ACFT TO A VERY SLOW TAXI SPD; AND THE TWR ADVISED US THAT THERE WAS AN AIRLINE FLT ON A 1 MI FINAL AND FOR US TO EXPEDITE CLRING THE RWY. THE TWR ALSO SAID THAT WE COULD USE RWY 9L/27R TO GET OFF. THE FO ACKNOWLEDGED THE XMISSION AND I REPLIED WE WOULD USE THE RWY TO TURN OFF. BECAUSE OF THE VERY LITTLE CONTRAST BTWN PLOWED VERSUS UNPLOWED AREAS; AS WELL AS THE SENSE OF URGENCY THAT ATC HAD PUT IN OUR MINDSET; AND THE FACT THAT WITH THE BLOWING SNOW IT MADE EVERYTHING GLARE AND BRIGHT; IT WAS HARD TO GET AN EXACT BEARING ON WHERE THE INTXN WAS FROM MY VANTAGE POINT. I ASKED THE FO IF WE WERE THERE YET; THINKING HE COULD SEE IT BETTER AND HE REPLIED YES; TURN! I MADE THE R TURNOFF FROM RWY 3L INTO A FLAT AREA JUST S OF THE INTXN FACING E. WE ADVISED TWR OF OUR SIT; THE ACFT WAS DIRECTED TO GO AROUND; AND THE RWY WAS CLOSED. WE USED A LITTLE PWR AND MOVED UP TO THE TXWY WITH NO DAMAGE TO THE ACFT. SEVERAL THINGS I HAVE LEARNED FROM THIS EXPERIENCE: 1) DO NOT LET ATC RUSH ME OR PUT ME IN A RUSH MINDSET -- ESPECIALLY UNDER LESS THAN IDEAL CIRCUMSTANCES. 2) DO NOT PUT ALL OF MY TRUST IN THE FO WHEN I AM IN THE UNUSUAL SPOT OF NOT EXACTLY KNOWING WHERE THE EDGE OF THE TXWY OR EXIT RWY LIES. 3) USE ALL OF MY CREW MEMBERS -- ESPECIALLY THE SO; WHO COULD HAVE BEEN VERY VALUABLE IN PROVIDING ANOTHER SET OF EYES TO CONFIRM WHERE WE WERE.