Squirrels aren't thick here anyhow but the snow keeps them either in the trees or in the den lots of times if it is a deep snow or one they can not walk on the crust. I have hunted close to the area that I imagine you hunt and I really like going down that way. I was hoping with the days of for Christmas I could get out that way but the snow has put a damper on that for me. I have had some very good days in the snow just was snow that was navigatal for the squirrels. This is my favorite time of year to go if you can get a good day because the squirrel will soon be chasing each other for the rut and with squirrel dogs this is a good time if they are out and the weather permits. Squirrel will be more apt to be out and running where it isn't their "home" and might not be familar with the den trees and nests in the area that they happened to find a prospective mate in and that can make for one very good day with squirrel dogs. Here is a picture of a good hunt that was in January from a few years ago and probably close to your area.
For the heck of it here is the first time Bella winded a squirrel, that is she treed the squirrel from the scent of it in the tree alone- the squirrel had not been on the ground and she didn't track it to the tree and tree it. She has gotten better since. This is also an old video.
For anyone interested, I don't have much on video but this can kind of give you an idea of what squirrel hunting with a dog is like. This happened to be a den tree but you can kind of see how I do it. Turn the dogs out they either go get treed or do a loop and come back to you. I either walk a little further toward where I want to head or stand and listen. When you hear them treed you go to them. If they don't get treed they come back and check in on you. I love it. I just wish we had more squirrels around here. It is pretty tough with a low population because the squirrels are all homesteaders and are familiar with the area and all the holes in the trees. If the population is high and the food is plentiful they move around a lot more. This video is about 4 minutes or so long.