Captain reported sliding past the stopping point on taxi to the gate due to icing conditions. Aircraft was pushed back to stop point.

Narrative

After landing in moderate snow we experienced medium to poor braking action on the runway. During taxi into the gate we were experiencing medium to poor braking action on the taxiways. The ramp area was better than the taxiway but still medium at best. We had to stop on the taxiway to give way to a plane going into the deice pad. We also stopped just before turning into the ramp. The ramp and taxiways were all covered with fresh snow making it difficult to determine the exit and to be sure we went well past and then back tracked to the gate area. We stopped again in the area about 2 or 3 gates away from our gate to allow a sweeper to finish sweeping our gate. After the sweeper cleared the area we proceeded into the gate. The turn into the gate was sharp and we didn't seem to experience any slippage of the nose tire. We cleared the area and proceeded in to park. I was very aware of the possibility of ice at the gate. I planned to arrive with minimal energy at the stopping point. When we were finally at the stop point and the marshaller signaled to stop I applied brakes to stop and felt a deceleration; however we never completely stopped. The marshaller again raised their arm and signaled to stop as I was pressing the brakes as much as possible. I realized we were sliding towards the terminal slowly. I released and reapplied the brakes but felt no difference and we continued to slide slowly forward. I then deployed the thrust reversers on both engines to idle reverse. The forward motion was stopped with the reverse thrust. I returned the thrust levers to idle and prepared to shut down. Before we could shut down the plane again started moving forward on the ice. I once again stopped the plane with reverse thrust. At this time we were past the opening of the jetway and I was very concerned that we would impact the jetway or other equipment. I held the reverse thrust longer and was in a slight dilemma; when the FO asked if he should shut the engines off? I said yes I think we will have to. As he started to shut them off I went to idle and the plane did not seem to move anymore. After a very long few minutes communication was established with the ground crew and we confirmed that they were okay and that there was no impacts or observed damage. We started the coordination to get the plane pushed back into position. I would estimate the distance to be 15 to 20 feet past the planned stop point.I would like to commend my FO for his quick assessment of the situation and the; now obvious; recommendation to cut the engines off. I hope I would have thought of that eventually but the situation was very disorienting. As a result of the reverse thrust being on just prior to shutdown a maintenance entry was made as the number one engine reverse blocker doors were not stowed. Cause: The first and most obvious recommendation would be to have the ramp prepared better before allowing any aircraft to try and park. My guess is that the brush truck actually cleared snow off of ice making the situation slightly worse. I would suggest a better assessment of the condition would be to try and drive a non chain equipped vehicle into the stopping area of the main aircraft tires.The FO fell twice on the ice while inspecting the aircraft. He said it was the worst ramp he had every tried to walk on. If this was the case before our arrival then we should have been held out for preparation of the ramp. Finally the use of the thrust reversers was my first thought and they were effective; however this is not a procedure that I have ever been advised of. It was simply my first reaction and only thing I could think of to stop our forward motion. In the future I will also think about being prepared to shut down the engines quickly in the event of slipping on ice.