I commute through a great deal of similar weather every year in Anchorage, AK.

The bike has full fenders and I always have a few chains lubed and ready to swap out. If they salt the roads COUNT on having some drivetrain parts die. It's a fact of life if you ride often enough in it. (they don't salt them here anymore that I'm aware of).

You get home, throw the chain into the solvent and shake, throw on the new one that's lubed, pull the chain that was drip drying into the lube container and hang up the cleaned one to dry. I like chainsaw bar lube for really nasty dirty/slushy conditions assuming you can let it drip dry overnight.

The outfit starts with a pair of combat boots and THICK wool socks. Warmer days get a pair of windproof/water resistant slacks over the pants I normally wear at work. Cold days get a pair of light waterproof snowpants (-30 or so is pretty much my limit for cold).

Top starts with a polypro tank, longsleeve poly shirt and a trench sweater. Colder days see a polarfleece jacket over this. I have an older pair of specialized "sub zero" gloves which are really more like gauntlets and they work well. On warmer days my hands often bake a bit but they really do a great job on even the coldest days.

Head is a balaclava and a giro semi-mx helmet (less vents and they're a lot easier to plug if it gets that bad).

Don't be afraid to wuss out if you're hurting. Better a humiliating ride with a friend or the bus than frostbite.