Air carrier Captain reported runway conditions were worse than reported during landing at ORD. Crew requested tow into the gate.

Narrative

During arrival into Chicago O'Hare International Airport (ORD); weather conditions were rapidly deteriorating; with a significant wind shift from north-northwest to north-northeast.We were initially cleared to land on Runway 27R; but this would have resulted in a tailwind component; and the reported runway condition code was 3/3/3. We executed a go-around and were subsequently resequenced for an approach to Runway 9C.While being vectored for the approach; approximately ten minutes prior to landing; the tower provided an updated report indicating that Runway 9C had a condition code of 3/3/5; with winds from 010 degrees at approximately 20 knots and no gusts. This resulted in a crosswind component below the 25-knot recommended limit for operations on a contaminated runway.The First Officer and I discussed the associated threats and concluded that; based on the reported conditions; an approach and landing attempt was acceptable.Upon touchdown; however; it became immediately apparent that actual runway conditions were significantly worse than reported. Braking action was effectively nil; and the aircraft repeatedly attempted to weathervane into the wind due to inadequate traction; resulting in several degrees of left yaw. Although I maintained directional control; the aircraft was on the verge of sideslipping. We eventually decelerated sufficiently to exit the runway.Conditions on the north-side taxiways were similarly poor. I taxied at a reduced speed until reaching the intersection of Taxiways Kilo and Tango. While attempting to turn onto Tango; the nose wheel lost traction; preventing completion of the turn. Rather than risk further maneuvering that could have led to departing the prepared surface; I stopped the aircraft; advised Ground Control of our situation; and requested tug assistance.A super tug was positioned behind us and received permission to connect. Initially; the plan was to use the tug only to realign the aircraft onto Tango. However; given the widespread ice; severely reduced traction; and uncertainty regarding conditions elsewhere on the airport; I recommended that the tug tow us directly to the gate. The tug crew agreed; assumed control of the aircraft; and towed us without further incident to Gate XX.