EMB-170 flight crew reported temporary loss of aircraft control during taxi out due to snow and weak braking action.

Narrative

While on Taxiway 1; in ZZZ in nighttime; snowy conditions on contaminated surfaces; we ended up becoming number 4 in line due to a disabled aircraft that required a tow off the taxiway and back to a gate. We and the other aircraft sat for over 45 minutes with both engines running due to slick airport surfaces; where braking action was less than good. When the line on Taxiway 1 started to move again; it started off fine; however; there was one point where the aircraft in front of us came to a stop. I applied brakes and thought that this was taking longer to stop than normal. I pressed harder on the full brakes and nothing was happening. At this point; I realized that we were; in fact; sliding towards the 737 in front of us. Unable to stop; I thought that it would be safer to try to turn the aircraft towards the left edge of the taxiway and possibly slide off the pavement instead of into another aircraft. I slowly began to turn the tiller thinking if I aggressively turned we would've continued to slide forward. I also applied the parking brake. The aircraft began to turn and slide in both directions forward and towards the edge of the taxiway; but came to a stop a few feet before the edge of Taxiway 1. My FO reported on Ground that [we] were sliding and eventually came to a stop; the aircraft in front of us at that time began to slowly move forward. We never left the taxi surface. When we had enough spacing; I was able to release the brake and slowly align the aircraft back up with centerline and continue taxiing.