My winter list for Chicago traffic riding:
Helmet liner: either a thin biking skullcap, or in worse weather a tight wool stocking cap. Or both.If I'm wearing a jacket with a thin hood, and it fits, I put that under the helmet if necessary.
Mirrors: I have used a Third-Eye Pro for years and love it. Chicago riding in traffic, I'm looking "backwards" half the time and can't afford to turn my head and miss what's in front, so it's a great accessory. Does vibrate a lot as Sstone512 says, but I also am fussy about things too near my eyes.
Eye protection: Pyramex safety glasses. Z87+ protection. Keeps the mirror out of your eyeball, available clear (night), yellow (dusk), sunglass grey. Buy anti-fog! Cheap enough to buy all three. These in particular look good off the bike, too,
https://www.amazon.com/Pyramex-Rende.../dp/B002PINHTG Read the reviews!
Gloves: I ride with ski gloves for two reasons: they come in many thicknesses, so you can pick by temperature, and they have traction on the palms. I often carry a lighter pair for when I warm up.
Clips: I ride with plastic toe cups. Best of all worlds for city riding. You can ignore them and ride with them down, or use them. Hiking boots fit. Handy in the city for jumping potholes, not too confining. Zefal Cristophe Mountain Bicycle Half Toe Clip--Amazon again.
Shoes: I wear Columbia Newton Ridge hiking boots in the winter. ***Very light***, very warm. Don't notice them. Good when you have to get off and walk.
rsbob's tool kit, for sure!
The best lock you can carry.
Lighting: in the city, something that flashes is more important than brightness. Don't skimp, whatever.
General clothing: I wear multiple thinner layers, sometimes as many as six. Tech fabric next to the skin. I ride with one saddlebag and shed layers as necessary. Sometimes I see people plugging along in four inches of feathers, and I can't see it--I'd be sweating to death.
The one thing I haven't figured out yet is rain gear. Eurostyle is a rain cape, out over the handlebars, and I like the idea, so I bought a cheap poncho to try this year. Last winter on foot I got caught out in a sleet storm without a hat----never again!!!