CORP ACFT TAXIES ONTO UNPLOWED TXWY. GETS STUCK.

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3 DAYS AFTER A HVY SNOW STORM/BLIZZARD WITH 2 FT OF SNOW; I TAXIED OUR CORPORATE JET OFF THE ACTIVE RWY ONTO A TXWY THAT WAS LIT BUT HAD NOT BEEN PLOWED. SHUT DOWN ACFT WHEN IT APPEARED SNOW WAS TOO DEEP TO CONTINUE TAXIING OR TURN AROUND. NO DAMAGE OR INJURIES. THE ACFT THAT LANDED TWO AHEAD OF US HAD TROUBLE FINDING TXWY TO EXIT RWY. NEEDED TO BE MORE AWARE OF TXWYS THAT ARE CLOSED; BY PAYING CLOSE ATTN TO ATIS AND LCL NOTAMS. INCLUDE IN CREW BRIEFING PRIOR TO LNDG WHICH TXWYS ARE OPEN AND CLOSED. AT NIGHT IT WAS HARD TO TELL IF TXWY WAS PLOWED OR NOT SINCE MOST EVERYTHING WAS COVERED WITH SOME SNOW. HAVE ARPT MGMNT BLOCK OFF CLOSED TXWYS LEADING TO/FROM RWY WITH REFLECTIVE CONES/BARRICADES OR LIGHTS. IT WOULD HAVE BEEN BETTER TO STOP ON RWY AND ASK TWR OR GND CTL WHICH TXWYS WERE OPEN. EVEN AT OUR HOME BASE WHERE THIS HAPPENED YOU CAN'T ASSUME IT WILL BE JUST LIKE THE LAST TIME. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES THAT THE ATIS HAD SOME INFO REGARDING THE UNPLOWED TXWYS BUT AT NIGHT AND WITH WHITE EVERYWHERE IT WAS HARD TO SEE THE TXWYS. THE ONE HE USED WAS LIGHTED; THE PLOWED TXWY WAS NOT LIGHTED. WHEN QUESTIONED IF HE HAD DISCUSSED THE USE OF CONES OR BARRIERS WITH LIGHTS; HE STATED THAT THE ARPT MGMNT WAS WELL AWARE OF THE SIT. THEY ARE THE ONES WHO HAD TO COME AND DIG OUT THE ACFT. WHEN HE RETURNED THE NEXT DAY THERE WAS MUCH MORE INFO ON THE ATIS AND GND WAS ASSISTING PLTS MUCH MORE. THE FAA INVESTIGATED THE INCIDENT; DETERMINED IT WAS AN 'OCCURRENCE' AND DROPPED IT.