Medium Large Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Ground Event / Encounter Other / Unknown
Human Factors; Weather; Airport
Arrival and landing at EWR were normal operations. We taxied via ground control to the ramp as normal and Ramp Control assigned 'direct access' as our gate arrival instructions.  At EWR 'direct access' refers to Taxiway Uniform.  As we approached taxiway Uniform we noticed that it was still covered with snow.  There were no NOTAMs or ATIS information that indicated this taxiway being closed.  The taxiway had obviously been used for normal operations.  I slowed the aircraft to mitigate any slipping or sliding.  I made the turn onto taxiway Uniform as we approached the gate the ramp agents held up an 'X' with the marshalling batons and I stopped the aircraft.  The aircraft became stuck in the snow at this point.  The ramp agents eventually hooked up a tug and pushed us further into the snow.  A snow plow truck tried to start plowing snow directly in front of us very close to the aircraft with the engines running.  We did not have communications with the ramp crew and I tried to wave the plow truck away from the aircraft.  I elected to shut the number 2 engine down as a safety precaution because of the plow truck.  The ramp agents then connected a different tug and towed us into the gate.
Taxiing into gate in EWR via the direct access through taxiway Uniform there was a section of unplowed taxiway that had obviously been taxied through already; so once we received a clearance from ramp we followed instructions. As we were taxiing on Uniform the rampers suddenly told us to stop and subsequently told us we were stuck as we were still moving. From there they did not allow us to continue out taxi they instead attached a tug; and had a snow plow try to plow around and under our wing while the number 2 engine was running. We shut down the engine to make the situation safer. At that point the plow was unable to remove any snow around the plane; so the tug started to pull us to the gate.
Air carrier flight crew reported becoming stuck in snow during taxi to their gate at EWR.