Or it is staying. I am currently on vacation in Norway between Bergen and Oslo and this afternoon it was snowing. In Finnse the whole area was still covered with snow, I guess at least 50cm.
Before we had, "Det er vår", so I'd say it depends upon whether you want to say just 'winter'/'spring' or 'the winter'/'the spring', the same as in English.
A specific winter (the one that is coming) is doing the action. It cannot be applied to just any winter, because there is only one winter that is (contextually) coming. Make sense?
I know that some people would be frustrated with your answer but I completely agree with you that sometimes things are the way they are simply because that's how they are. English probably has many more of these than norsk does.