CARGO LTT BECOMES LOST WHILE TAXIING TO RAMP IN SNOWSTORM.

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AFTER LNDG (DURING RUSH PERIOD) AT EWR ON RWY 4R; WE CLRED AND CONTACTED GND CTL. ALL RWYS AND TXWYS WERE COVERED WITH APPROX 3 TO 4 INCHES OF SNOW (A STORM WAS IN PROGRESS). WE (THE CREW) WERE UNFAMILIAR WITH THE ARPT AND WERE ATTEMPTING TO TAXI TO THE COMPANY CARGO RAMP AND OFFLOAD OUR CARGO. WE INFORMED GND THAT WE NEEDED TO TAXI TO COMPANY AND REQUIRED A PROGRESSIVE TAXI. GND CTL WAS EXTREMELY BUSY AND THEY RESPONDED BY ISSUING THE FOLLOWING -- TO OUR ACFT...FOLLOW THE ACR EXPRESS ATR-42 TO YOUR L; PROCEED VIA THE INNER TO R/B TO RAMP. AS INSTRUCTED; WE FOLLOWED THE ATR -- AND HAD NO FURTHER CALLS FROM GND. AS WE FOLLOWED THE ATR; HE MADE A SLIGHT L TO THE OUTER TXWY AND WE FOLLOWED; AS IT WAS IMPOSSIBLE TO READ TAXI SIGNS COVERED IN THE ICE AND SNOW. WE ENDED UP IN A BAD POS BY THE DE-ICE PAD AND A STACK OF ACFT IN LINE FOR 4R. WE CALLED GND AGAIN; AND AFTER SOME CONFUSION AS TO OUR LOCATION(THEY COULDN'T SEE US DUE TO LOW VISIBILITY) WE WERE ABLE TO MANEUVER OUT OF THE WAY AND PROCEED TO RAMP. CAUSE: FATIGUE; LACK OF SITUATIONAL AWARENESS; LACK OF HELP BY GND CTL; AMBIGUOUS TAXI INSTRUCTIONS.