There is no bad weather, just bad clothes.Traditional saying
There are three main ways I like to enjoy the winter forest.
The first is taking a walk or run. If I run, I use winter gear including trail shoes that are just shy of being cleats; which is still no particular insurance against ice. If I walk, I may take the dog with me, and I put her jacket on her as well as protective gel on her paws before we go out.
The second way is taking photos. My favorite thing is hoar frost which does not happen as often. Someday it would be fun to get into wildlife photography.
My third way is to put out some extra dried cranberries, suet, or what have you, at the bird feeder because it is rather slim pickings for the small birds after a big snow or ice storm. They enjoy the extra calories, and I enjoy watching the increased number and frequency of different species visiting. (And practicing some citizen science on Merlin Bird ID App by Cornell Lab as a citizen ornithologist, aka amateur birdwatcher.)
I’ve always enjoyed winter in the forest for the decrease in color and the accompanying increase in texture and contrast. It also makes the Great Indoors more fun when it is inclement out. A roaring fire and hot drink is the way to go.