While many larger and more traditional museums aren't dog-friendly, there are certainly a few fun ones that are, such as the Museum of Dog in North Adams. It's not particularly big but there is still a ton to look at and you'll be able to stay comfortable and warm inside while you do so.
It might be cold and it might be snowy but that doesn't mean you can't bundle up and see a new side of your favorite dog parks. Some dogs love frolicking in the snow but rarely get a place or time to do so. Wrap yourself and them up good if need be and see some new sites in your old favorites.