I come from "Up North Minnesnowta" So maybe I can give you a couple tips:
1. The probability that the medical school student or person giving the tour will make you go outside is very slim. At the U of MN tunnels were created to avoid going outside at all costs in the frigid cold, we call ourselves gophers for that reason, seriously.
2. Elegant off-white coat will look great. It will probably match the snow. Also, most physicians that I work for wear winter parkas. when it is cold, people do not judge and do what they can to stay warm.
3. In regards to the shoes, I would be less worried about your toes being cold and more worried about walking up steps or on concrete getting to your interview. In MN I slip and fall all the time wearing my winter boots made out of rubber. I would advise wearing shoes with a lot of traction to the interview and then just changing into your professional shoes at the interview (once your safely away from the ice). Most interviews I have gone to in the midwest this winter have had expansive coat racks where you could place the boots.
One final tip for ANYONE going up here in the midwest is salt on the sidewalks. Do NOT place your shoes that you have walked on the sidewalk with anywhere near your black or navy suit/outfit. Also watch when you are exiting your vehicle to be careful not to rub your leg along the car door. This will result in white salt powder on your suit/coat/outfit.
If you are going to an area with snow, this is what you will probably be walking through at some point if it is a typical winter day: (look closely at trouser's pic). I am not sure where your interview is and these tips should not scare you, but just be aware that the sidewalks are slippery, it is very cold, and nobody will judge you for wearing a warm coat over a fashionable one, especially because you will be taking your coat off.
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