A FLT CREW INADVERTENTLY TAXI OFF OF A TXWY DUE TO SNOW BUILD UP ON THE TXWY AND SIGNS.

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AFTER LNDG ON RWY 6R AND EXITING THE RWY ON TXWY G. I WAS ADVISED TO TAXI ON G; CROSS RWY 6L TO TXWY E; AND TAXI ON THE TERMINAL RAMP TO CUSTOMS. AFTER I CROSSED RWY 6L ON A WELL-PLOWED RWY AND TXWY AREA I ENCOUNTERED A COMPLETELY WHITE OUT AREA ON THE INTERSECTION OF RWY 6L; TXWY G; AND TXWY E. THE TXWY SIGNAGE WAS UNREADABLE DUE TO SNOW COVER ON THEM. I INADVERTENTLY CUT THE CORNER SHORT BETWEEN TXWY G AND TXWY E; TAXIED THROUGH ABOUT FOUR TO FIVE INCHES OF LIGHT SNOW ON A FROZEN SURFACE. I ENDED UP ON TXWY E1 AND TAXIED TO THE CUSTOMS RAMP. NO DAMAGE WAS NOTED TO THE ARPT LIGHTING OR ACFT. ANCHORAGE SNOW REMOVAL DOES A GREAT JOB FOR THE MOST PART; BUT PERHAPS SHOULD TAKE A LOOK AT GIVING MORE ATTENTION TO THE INTERSECTION MENTIONED. WITH LARGE ACFT SUCH AS B747 AND DC10 TAXIING OUT FOR DEP ON RWY 32; THEY TAXI UP TXWY E AND AS THEY TURN THE CORNER THEY TEND TO DRIFT THE SNOW AND CAUSE THE WHITEOUT CONDITION AT TXWY G AND TXWY E INTERSECTION; ALSO BLOWING SNOW ON THE SIGNAGE MAKING IT ILLEGIBLE. CONTRIBUTING FACTORS: 1) FATIGUE DUE TO A NINE-DAY INTERNATIONAL TRIP. 2) POOR VISIBILITY DUE TO ICE FOG.