Another approach - a different bike. My preferred winter bikes in my Boston days were fix gears. Where the setup was such that all day in the drops worked. Very little bare metal needs to be touched. The grip on the drops has no specific hard points so circulation is better. And fix gear - cold coasting doesn't happen. Downhills are slower; less cooling and much warmer; you are generating considerable heat.

If you haven't ridden fix gear, don't make the change now! Cold weather is NOT the place to learn! But consider setting up a good winter fix gear next summer and riding it. When next winter happens, you'll see why it's been a winter favorite for so long.

And a specific item that makes for far warmer hands - the Zzipper fairing. Better done on fix gears than briftered bikes. (Yes, you look goofy but you will be a full layer of clothes warmer, wind is completely off your hands and the bike is one tooth faster. Quartering tailwinds are serious fun!)

I hail from Portland now, but I've wintered in Boston and Ann Arbor without a car Spent a lot of time doing all of the above..