Winter wear and winter weather etiquette for Chicago noob?

EDIT/UPDATE: I am so overwhelmed and grateful that SO many people took the time to comment on this post and share their experiences, advice, and wisdom with me. It means so much that so many went out of their way to give me a warm welcome to your beautiful city!! Honestly, it means so much, thank you. 😀

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Hey Chicagoans and Chicago experts!

TL;DR - Asking for Chicago-specific advice and etiquette relating to cold weather and winter clothing for when I move to Chicago in February!

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For context, I am a consultant, and I will have to commute into the loop at least once or twice a week. That will involve a 1 mile walk to the Metra station, walking from the downtown station to my clients' office, walking around midday for coffee and lunch in the city, often with clients, and then walking to and from the Metra on for my commute home. I'm coming from a part of the country that has a fairly mild winter. I grew up in an area with snow and snow sports within day-trip distance, but really haven't had to deal with cold and/or snow on the ground day-in and day-out for months at a time. So, I know how to dress for snow sports, but I'm thinking that style isn't going to be entirely appropriate for city life.

Underlayers: So far I've been focusing on layering, making sure that I have a week's worth of soft, neutral colored, moisture-wicking base layers that can be worn under any long sleeve top and wide leg pants or a suit - think tank top, coordinating fitted long sleeve top, fitted leggings, and slightly larger lined leggings with a smooth outer fabric. I feel pretty good about that, since these are clothing items that won't be visible. My only concern will be getting too warm while in the office, but I could always go to the ladies' room, undress, remove my second/warmer layer of underclothes, put them in my bag, and put my office clothes back on. Sounds a bit exhausting, but it beats freezing on my commute I guess!

Outerwear: This decision seems more high-stakes since it will be the first impression anyone has of me out of doors or entering a building. I'm now shopping for a coat, and I'm thinking a neutral puffer coat would be pretty versatile and warm. Curious though, is a puffer coat appropriate for the downtown corporate environment, or does it seem more like weekend wear? Should I instead go with a long, belted wool coat as my winter outerwear staple, or some other option? Can I really get away with wearing the same coat every day, assuming that I accessorize it with different hats and scarves, or do I need to have at least two coats to switch between? If anyone has a favorite go-to brand for work-appropriate women's coats I'm all ears!

Shoes: I did an internship in NYC (though it was over 15 years ago) where I saw people wear snow boots to commute and walk in to the office and then switch to a work-appropriate shoe once they are in the building. Is that something people typically do in Chicago as well these days? Where does this footwear switcheroo take place, and where do people like me (who don't have a dedicated office/desk in the building) store their snow boots during the workday? One thought I had was to get a gym membership in a central downtown location, close to my clients' offices, and rent a locker in the locker room where I could shed my practical winter gear for some professional footwear. Is that overkill? Again, brands would be helpful here if anyone has advice for women's shoes/snow boots for work days.

Etiquette: Coming in from the cold, my face is typically red, my lips are blue, my nose is running like a faucet, and my hair is disheveled and staticky from my hat and scarf. I don't really want to walk straight into the office looking like that, unless that's what everyone does? Is it expected that people disappear into the restrooms to touch up their makeup and hair after their commute or their lunch hour, or will I appear fussy if I do that? What about hand-shaking when first walking in from outside? Remove one or both gloves, shove the gloves into a purse or coat pockets, then shake hands? Also, and finally, is it okay to ride the Metra and walk around with a thermos of hot coffee in and out of the office? Can I bring my thermos to local coffee shops and ask for refills, or should I leave it in my bag for lunch and coffee breaks? Does it have to be some trendy thing that matches my outfit, or can it be basic and serviceable?

Identity and Belonging: When does one "become a Chicagoan"? In New York they like to say it takes least ten years to become a New Yorker. Any similar "belonging gatekeeping" in the great white city, the urban jewel of the Midwest? I grew up visiting my grandparents, aunts, uncles, and cousins in Minnesota (my parents' birthplace), and I definitely have the slightest hint of an accent - enough for people to ask constantly if I'm from Minnesota, lol. Not sure if that will help me blend in once I get to Chicago or just make me sound like a Minnesotan, but hey, guess I'll find out! :)

Thanks so much if you read this far. Any help and advice would be greatly appreciated!