Parka? Lord no.
Buy a nice overcoat, most any decent one will do. Mens warehouse tends to look like mens warehouse, but for an overcoat, itll probably do. Personally I like the loden style, but its very hard to describe and i cant find a darn thing online - so dont go searching for loden unless you know what it is and what I mean.
In short, yes, its very cold in chicago right now - my car read -4 last night, and windchills are hitting -20 today. It wont stay this way - this is beyond normal - but it will be cold when you visit. A suit will not keep you warm.
I suggest a full length coat, at least to the knees, not something that stops at the waist. For instance:
https://www.saksfifthavenue.com/main/Pro ... 0640414391
Beyond that - No zippers, wool or cashmere, but not Stay classic look. It should look something like this on top of suit:
https://www.eshopone.com/images/overcoat ... detail.jpg
or like this:
https://www.indrafashion.com/images/men/ ... ercoat.jpg
(but i dont like brown personally)
or
https://www.mycustomclothing.com/images/shop/7817.jpg
(this is a shorter one, I think longer ones look much much better).
This is a terrible picture, but this is a good look:
https://www.customclothiers.cc/images/shop/339.jpg
Generally speaking, single breasted four button is safest best in my mind.
Beyond that, its very simple to deal with. When you get to the interview, they will likely offer to hang your coat up. If they dont, you simply take it off, drape it over your LEFT arm (if you stay standing up), and wait for your interviewer. When he/she shoes up, shake hands (this is why you drape over the left, not the right arm), and then place it on the back of your chair.
Easy as pie.
But for hte love of god.... no parka.