Still plenty of stuff to do in the winter! Trees die off and you can find old mine camps and stuff better. You can walk creeks and rivers to find surface floaters. I go to the Arkansas River right under the highway and pick up all kinds of petrified wood and smoky quartz for example.
Sure, its not as cool as digging in or tinking, I know. Although there's got a Topaz mine I have access to that goes about 40 yards into the mountain that cold weather shouldn't be a bother in... It would be my first time going into a mineshaft in winter so im completely talking out the side of my head, speculating.
Just trying to be positive!