Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 147; Flight Crew Type 7728
Ground Event / Encounter Loss Of Aircraft Control; Ground Excursion Taxiway
General None Reported / Taken
Weather
FO leg. Got ATIS multiple times enroute. Not great; but certainly not horrible. Runway [was reported] 90% clear and damp; 5% treated; 5% packed. Remember remarking how much better these guys are equipped and efficient with their winter weather operations and reporting. Had other runways conditions also broken down by percentages. Discussed the approach and landing and taxi plan at length. Uneventful descent; approach; touchdown. Winds slight left to right I believe. RJ landed in front of us. Tower tells us braking reported good.During rollout; after my 80 knot call; we swap controls. FO passes letting me know that the brakes are still on. I roger that and apply pressure to release and now can check for myself the braking. The runway certainly did not look 90% damp and clear; but we were in good shape. Braking initially did; in fact feel good and responsive. I remember seeing a 90 degree turnoff and thinking that I could have made that; but why? There is our briefed and easy high-speed ahead.Continued to brake and now pump and steer to exit. Things begin to not go as planned quickly. I am now unable to turn or stop. Straddling the turnoff and runway; I vividly remember that I now must commit to taxiway or back to runway. I made the decision to continue with my turnoff since all of my effort was going in that direction. I am now furiously working with feet and nose wheel to get this thing going in the right direction. At the very last; the aircraft responded to the right. Perhaps a dry patch from ice. Do not know. My dilemma was not over. With full nose wheel (I think) and rudder; the craft now just could not respond to the immediate left that I so desperately needed now to right itself on the high-speed.I continued the struggle for my full left; finally getting response; but not until we had departed on the right side of the taxiway. We trundled along; my steering gaining purchase finally; and barely; until we came to rest facing east; or close to it; on an intersecting taxiway.
[Report narrative contained no additional information.]
B737 Captain reported departing the high speed taxiway after clearing the runway due to ice and snow on the surface.