Air carrier First Officer reported difficulty with directional control and NIL braking during landing. Flight crew notified the Tower.

Narrative

As we approached ZZZ; the weather deteriorated rapidly. We had to swing around to an East runway due to tail-wind limitations. Low Visibility then also came into play. We consulted the crosswind guidelines in the flight manual and received both the runway condition codes and a braking action report from a jet ahead of us. We also received landing data. We double checked winds on initial check in with tower and again at 1;000 feet. We stayed within published flight manual guidance for the given winds & braking action. We touched down on the runway (it was lightly covered in snow); and had difficulty with directional control and deceleration. As we rolled out; we worked as a team to maintain directional control and get the aircraft stopped. We notified the tower that breaking was NIL. No one was injured and no damage to the aircraft. We never left center-line but the aircraft was trying to turn into the wind despite proper corrections and low use of reverse thrust.