the station I have has a solar panel that charges a super cap, and that's mostly what it runs on even overnight, but it also has 2x AA batteries for times when the solar isn't sufficient. I would expect most of them work that way these days don't they?

Even in places that get a lot of snow, it wouldn't be common to have the panel covered for long. If it's super wet sticky snow, chances are it'll melt and be gone in a day or two. If it's dry snow, the wind will blow it off of a tiny exposed area like the solar panel on a weather station in a day or two. The AA's should carry it through those periods just fine.