I've got an article on this subject in the current (January) issue of Michigan Out Of Doors-you might want to take a look at it. Hunting squirrels in the snow and cold is not new to us up here in northern Michigan...we can just hunt a little longer this year.
I'm hunting this month, but I'll probably lay off them as of 2/1-I want to make sure we leave plenty of seed.
After a storm, wait for the first calm, clear morning. Calm is imperative. Get out there right after daylight, in areas that you've seen RECENT squirrel sign-in northern MI right now, because we have such a rotten hard mast crop, that's around corn fields. Wear snow camo, if you can, or match the surroundings as much as possible, wearing only the required amount of orange.
I carry a .22 rifle loaded with copper-coated magnum hollow point loads-I like the Velocitors and CCI Long Rifle Mags. A cheap deer scope makes all the difference.
Blend into your surroundings as much as possible, and find a good spot to sit. On a good morning, you should see squirrels moving within 10 minutes, but don't look for them on the ground much if you have more than six inches or so of snow. Silence is mandatory.
Study trees carefully, looking for bits of ear, tail, etc., rather than the entire animal.
Prepare for long shots, and usually, you'll only get one, two if you're real lucky.
Don't be surprised if you only see a handful of squirrels in the areas you saw dozens in earlier in the fall-squirrels are conservationists of energy in the winter, and don't move around more than they have to.
I don't use squirrel calls in the winter, as I've found they serve more as alarm calls than anything else when it's cold out. I'm looking forward to getting out with someone's squirrel dog soon, I hope. Will be interested in seeing how they do in the winter.