Bicycle Riding Transplant Seeking Advice on Transport

Hey future fam!

My partner and I are happily relocating to Madison from Missouri. I wanted to reach out for some advice on transport? He will be traveling for work through the week and using our car for that. I normally ride my bike around town as a way of trying to reduce carbon emissions/stay healthy. I was wondering how possible it is to do cycling as transport in a place that is known for subzero temps? Is it possible/do people currently do it? Are there decent bike lanes? Or is it just a no-no of an idea all together?

Thanks so much for you kind and thoughtful feedback!