Pilot reported poor to nil braking action after landing at an airport in mountainous terrain.

Narrative

Enroute from ZZZ1 to ZZZ we were aware of ZZZ being below minimums due to low visibility and +SN. As ACARS was MEL'd we contacted Company Dispatch via Crew Phone and discussed both the weather and field condition as per NOTAM with plans to divert to ZZZ2 if the weather did not improve. At the time we were unaware that we would be the first large jet to arrive other than GA and corporate jet traffic. Braking action reports on descent indicated that the runway was acceptable for landing as well as a reported 5/5/4 FICON (Field Conditions). Per the company app we used current conditions (Braking Action 4) and ZZZ short field data to compute our landing distance; showing distance was acceptable for landing based on reports. Weather improved prior to descent and we commenced the approach and met all necessary performance gates per the approach plates and Company. ZZZ weather had improved significantly and visual conditions were achieved at approximately 8;000 MSL. Winds were variable due to snow squalls in the area and alternated frequently on the airfield; not unusual for mountain flying and ZZZ in particular. Also; the FO (First Officer) had to make a small lateral maneuver on final to avoid a flock of geese at our 11 o'clock position. We had thoroughly discussed the need to touch down in the first 1;000 ft of the runway. As the FO was an experienced type aircraft pilot and also experienced into ZZZ (more so than I regarding recent ZZZ operations) I remained PM Pilot Monitoring rather than assuming the PF (Pilot Flying) duties for landing which would also allow me to monitor the approach and landing closely. While winds were varying from quartering headwind to tailwind down final they dropped off around 200 ft AGL which is where I transitioned to outside references. The aircraft was configured and stable at touch down and medium autobrakes had been selected with the plan to begin max manual braking after touch down. We felt that we had touched down within the prescribed first 1;000 ft of the runway (data subsequently indicated touchdown logged at ~1;300 ft HOWEVER runway markings were not visible to us due to recent contamination and clearing operations were ongoing based on arrivals) and the FO began max manual braking along with selecting maximum reverse on the engines. I personally noted a slightly less than optimal deceleration but attributed it to the runway condition. We had passed the turnoff and continued slowing when the FO remarked that the aircraft did not seem to be slowing as he expected. I assumed control of the aircraft and ensured maximum braking was selected; at some point around this time we received a ROP alert (Runway Overrun Prevention System). I also noted that braking was only marginally effective and worked to ensure the aircraft remained on centerline. I also selected idle thrust as CFM reversers are basically ineffective at slow speeds and I wanted to ensure directional stability. We slowed the aircraft to a stop on centerline and I estimate we had less than 200 ft feet of runway remaining at stop. I would rate actual braking action between poor and nil (Braking Action between 2; at best) in the last third of the runway. We carefully exited the runway at the end and taxied to the gate; informing tower of our estimated braking action as Braking Action Reports were in effect. Taxi in was uneventful. After our departure from ZZZ to ZZZ1 I forwarded our actual braking report to ZZZ2. At least two inbound air carriers on frequency elected to either divert or hold based on that report. We had no such luxury and in the parlance of my previous military flying we were effectively a 'weather ship'. In over XX years as an [aircraft type] Captain; I have had no landing performance events that came as close as this one to experiencing an excursion and only once as a military cargo pilot operating on short; unimproved airfields.Causal factors would include recent weather at ZZZ resulting ina contaminated runway surface; lack of actual braking reports from large transport category aircraft; a relatively heavy aircraft due to necessary fuel requirements (including additional Ferry fuel) coupled with a high altitude airport and relatively short runway; variable winds at the airport; a touchdown that we now know was potentially long based on company requirements and questionable validity of the FICON measurements. Also; I was assigned this flying as a Recovery Obligation trip due to company crew scheduling pulling me off of my published trip and reassigning me the ZZZ flying. The last time I personally flew into ZZZ was in favorable conditions and almost 2 years ago.In retrospect I would have briefed a touchdown as close to runway threshold as possible as that is the primary thing that would have provided us an additional safety pad on rollout. Also; we queried the Tower Controller as to the 5/5/4 FICON as opposed to actual braking action reports and he stated he was obligated to provide the reports as they were given by the measuring equipment. I consider the reported FICON as being unreliable; particularly the /4.