Air carrier Captain reports taxiway excursion from icy taxiway during taxi to the gate after landing.

Narrative

At the end of the rollout; I took control of aircraft after Tower directed us to stay with him to the gate. Tower gave information that another aircraft had reported poor braking on one of the taxiways. Therefore; I brought the aircraft to a stop to power onto the first taxiway. The first taxiway was Taxiway F and after a stop and start; braking appeared to be fair. Then I turned onto Taxiway A at a walking speed. Initial entry was fair until the centerline and then it became nil. Full tiller movement and various levels of braking had no impact. The nose gear departed the prepared surface with the nosewheel at maximum left. The aircraft came to a stop due to snow piling up in front of the turned nosewheel. After all passengers were deplaned and taken to terminal; I inspected the aircraft and could not find any damage. The nosewheel was turned to maximum limit but did not appear to go beyond it. A taxi light was hit and that had to occur from the nosewheel. No damage noted to any other area of aircraft. The aircraft was on a nil surface with a 10-12 KT wind. When landing on Runway X; the normal taxi route to the terminal is Taxiway A. When conditions deteriorate; the airport should test the common taxi routes to parking. I understand this will probably be only one route due to workload; but if there are no non-nil routes to the terminal and the runway is good; the airport is essentially shut down for air transport operations.