EMB-175 Captain reported temporary loss of control while taxiing off the runway due to weather vanning in strong winds at a snow covered airport.

Narrative

I was the Captain operating Flight ABCD from ZZZ1 to ZZZ. Forecast and observed weather in ZZZ included snow; reduced visibility; and strong surface winds in the 20-kt. range gusting up to 51 kts.; with conditions fluctuating near approach minimums. Prior to departure; I messaged Dispatch requesting notification if visibility dropped below minimums so we could begin slowing early to conserve fuel if necessary.After takeoff and leveling off; we obtained the automatic digital ATIS; which reported weather at approach minimums. While being vectored to final; a new ATIS was issued reporting visibility of 1/4 mile. RVR at the midpoint and rollout was above minimums; but touchdown RVR was inoperative. We discontinued the approach to verify approach legality with dispatch. During the subsequent vectors; visibility improved to 3/4 mile; and we prepared to attempt the approach again.Approximately 15 miles from final on the next attempt; we received a Dispatch message advising us to divert to ZZZ2 due to a reported power outage at the ZZZ Terminal. We again discontinued the approach. Approach Control advised that power had been restored approximately 20 minutes earlier; and an airport operations manager on frequency confirmed that terminal power was restored. Given that our planned alternate was ZZZ3 (not ZZZ2); and to avoid unnecessary fuel uncertainty; we elected to attempt the approach again with the plan to divert to ZZZ3 if unable to land.We set up for the approach a final time; acquired the runway visually; and landed without incident. Winds had decreased to gusts in the 30-knot range with minimal crosswind component. We sent landing numbers using a runway condition code of 5/5/5. Braking action during landing was medium to good. In hindsight; a more detailed discussion of the reported runway conditions and consideration of a more conservative runway condition code may have been appropriate.After clearing the runway at Taxiway 1; which was the only available taxiway due to ongoing snow removal operations; the aircraft began to skid despite a taxi speed of approximately 5 kts. As we continued onto 1; the skidding increased and the aircraft began pulling to the right. Full left tiller input was applied; however; the aircraft continued to drift right and off the taxiway centerline. I applied full brakes and set the parking brake.After releasing the parking brake and attempting to taxi again with full left tiller; the aircraft again pulled to the right. The First Officer identified that strong winds were impacting the vertical stabilizer and causing the aircraft to weathervane. We agreed to reset the brakes and reassess the situation before further deviation from the centerline.We informed Tower that we were unable to move on 1. Tower acknowledged and asked if assistance was required. We coordinated with Operations regarding the availability of a tug; however; they advised they were occupied with ramp snow removal and jet bridge malfunctions and could not provide an estimated time of assistance. We informed ATC; the flight attendants; and passengers of the situation.After approximately 10 minutes; an airport operations vehicle arrived to assess the aircraft. I communicated with them to determine whether snow accumulation was preventing movement. They advised the aircraft should be able to complete the turn and offered to provide additional personnel to marshal the aircraft. With airport personnel in position to monitor the aircraft externally; I briefed the First Officer on a plan to counteract the wind by holding left brake; slowly releasing right brake; applying asymmetric thrust to the right engine with the left engine at idle; and maintaining full situational awareness. The First Officer agreed with the plan.The maneuver was executed as briefed; allowing the aircraft to realign with the wind and taxi safely to the ramp. We proceeded to the gate without further incident.Lessons Learned.This event reinforced the importance of anticipating wind-induced weathervaning during taxi operations on contaminated surfaces; even at very low taxi speeds. It also highlighted the value of stopping early to reassess; utilizing available resources; and employing deliberate CRM and clear communication with ATC and airport operations to resolve the situation safely.