TXWY EXCURSION BY ACR FGT WITH TXWY CONDITION SNOW. UNEXPECTED OBSTRUCTION OF SNOW BANK ENCOUNTERED DURING TAXI.

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FLT DUTY PERIOD BEGAN AT MSP. SCHEDULED DEP WAS AT XX10 AM; FEB/93. SDF WAS CLOSED BECAUSE OF SNOW AND FOG. WE CALLED DISPATCH AND WERE TOLD TO STAY IN MSP UNTIL THE FIELD AT SDF OPENED. WE WERE LATER TOLD THAT SDF STAYED CLOSED BEYOND ITS PREDICTED OPENING OF XX00 AM BECAUSE A SNOW PLOW WAS STUCK ON THE RWY. WE FINALLY DEPARTED MSP AT XZ32 AM; TAXI TKOF AND ENRTE TO SDF WERE NORMAL. AN INST APCH TO RWY 1 AT SDF WAS FLOWN; LNDG WAS NORMAL. ROLLOUT WAS NORMAL. WE ASKED IF WE COULD CLR ON RWY 29 AND TWR TOLD US THERE WAS 'VIRGIN' SNOW. THE NEXT TXWY C HAD SOME ACFT TRACKS SO WE CLRED THE RWY THERE AT THE INTXN OF TXWYS C AND G. THERE WAS A 'WIND ROW' OF PLOWED SNOW TO THE L AND A PATH OF TIRE TRACKS TO THE R. THE CTRLINE COULDN'T BE SEEN. I FOLLOWED THE TRACKS AND THE R MAIN GEAR WENT OFF THE EDGE OF THE TXWY. I SHUT DOWN THE R ENGS; CALLED GND AND WAITED FOR A GND TOW. I FEEL THAT AT LEAST THE CTRLINE SHOULD HAVE BEEN PLOWED AND THE 'WIND ROWS' COMPLETELY REMOVED NOT JUST PART OF THEM. THE PERCEPTION WAS THAT THE PLANES BEFORE WERE ABLE TO USE THE R SIDE OF THE TXWY. SUPPLEMENTAL INFO FROM ACN 234252: SDF ARPT WAS COVERED IN SNOW AFTER A HVY SNOW STORM; AND UPON LNDG WE NOTICED THAT BASICALLY ONLY THE MAIN RWY (1/19) HAD BEEN PROPERLY PLOWED. ON ROLLOUT; THE FO ASKED THE TWR IF WE COULD TURN OFF AT RWY 29 (WE LANDED TO THE N). THE TWR TOLD HIM THAT IT WAS NOT POSSIBLE AS RWY 29 HAD NOT BEEN PLOWED; AND ADVISED US TO TAKE TXWY C OR D.