It may not be apparent to some on here, but the TV forecasts which are deterministic, only give the forecast for the most likely scenario. Since weather forecasts are not perfect, and therefore have an error distribution associated with them, if the forecast says expect 5-10cm of snow overnight, there is a non-zero probability that the snow could be 15cm, or 20cm. I don't know the ins and outs of operating a railway but I suspect the railway can cope with some snow but there is a point where if enough snow falls, things start to go tits up. For those responsible for making the decisions, they have to make a decision based on the probability that the snowfall will be high enough that it is better to shut services down rather than try to battle through and deal with all the chaos (they will know from past experience how much snow the network can take before it falls over). If that probability is greater than some threshold they will make the decision in advance not to run services and inform people who can then (if possible) make alternative plans.
Am I in any way close as to how decisions are being made right now?