MLG STRANDED AFTER FLC RAN INTO A SNOW BANK ON RAMP AREA TAXIING TO PARKING.

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I WAS LINE CHK AIRMAN CAPT IN R SEAT GIVING SUPERVISED OPERATING EXPERIENCE TO NEW CAPT WHO WAS TAXIING AT TIME OF INCIDENT. WE HAD A NORMAL WINTER OPS LNDG FOLLOWED BY SLOW TAXI CONSIDERING SLICK TXWYS AND RAMP. AFTER LNDG RWY 6 WE TURNED OFF AT TXWY H AND TAXIED ON TXWY E TO THE RAMP AS INSTRUCTED BY GND CTL. ONCE ON THE RAMP WE HAD TO GO NW BECAUSE OF NUMEROUS SNOW PLOWS AND ARPT VEHICLES. WE WERE INSTRUCTED TO CONTINUE TO TAXI AS WE WERE; AND FOLLOW ANOTHER INBOUND ACFT TO GATE WHEN WE ENCOUNTERED A SNOW BANK LEFT IN THE TAXI ZONE. TXWY/RAMP EDGE LIGHTS WERE IN VIEW AND WE WERE TAXIING WHERE WE SHOULD HAVE BEEN. THE #2 ENG INGESTED SNOW; FLAMING IT OUT AND THE R MAIN LNDG GEAR ALSO WENT APPROX 2 FT DEEP IN THE SNOW. WE WERE TAXIING VERY SLOW AT THE TIME SO STOPPED QUICKLY BUT SMOOTHLY. WE SHUT DOWN BOTH ENGS AND CALLED FOR HELP TO DIG US OUT. THE RAMP WAS COVERED WITH SNOW AND CAUSED A TOTAL 'WHITE OUT' OF ANY SNOW BANKS ON RAMP. ARPT POLICE AND ACR STATION OPS PERSONNEL COMMENTED THAT ARPT VEHICLES HAD BEEN RUNNING INTO SNOW BANKS ALL DAY BECAUSE THEY COULDN'T SEE THEM. GND CTL WATCHED US TAXI AS INSTRUCTED AND OBVIOUSLY DIDN'T SEE THE SNOW BANK EITHER; TO WARN US. SNOW WAS PLOWED TO CTR OF TAXI ZONE AND NOT OUT TO THE EDGE. BAD PLACE TO LEAVE IT AND DID NOT WARN US. WE COULD NOT TAXI ANY CLOSER TO TERMINAL BECAUSE OF PLOWING OP AND A LARGE SNOW BANK THEY WERE WORKING ON.