B757 Captain reported the aircraft slid on taxiway during a turn due to surface conditions. The aircraft was towed to a different taxi route to continue taxi and the flight eventually departed.

Narrative

We were cleared to taxi to Runway X in ZZZ after deicing in snowy conditions. We taxied north from the ramp on Taxiway 1 and at a slow ground speed I initiated a left turn on Taxiway 2. After completing the turn the airplane continued to turn left and the airplane also kept moving forward with the brakes fully applied. I immediately went to idle reverse which significantly help to stop the airplane. After stopping; the airplane was angled towards the left close to the left edge of Taxiway 2. We called ZZZ Tower to let them know we may have departed the taxiway and that we needed to be towed by our company. The ZZZ fire/rescue crew and Air Carrier maintenance both arrived at the aircraft and verified that the airplane did not depart the taxiway. Since we were still within the holdover time range and we had more than the required fuel I decided that we could continue the flight. We requested and received clearance to have maintenance tow us in a safe position where we could start a different taxi route to Runway X (via Runway XX/YY to Taxiway 3). The new taxi route had adequate traction and we continued the flight uneventfully to ZZZ1.The cause was due to taxing on a surface that was not conducive for suitable traction