Well, in Chicago you pretty much bike on the good days. The infrastructure isn't great (like noted by OP in his followup to me) - but the density of the city makes it pretty workable if not entirely enjoyable. You can typically get around on bike on the good weather days faster than most other forms of transit - largely because you're only a few miles from anywhere you need to be.

So in Chicago the typical bicycle commuter commutes on the nice days (maybe half the year?) and will take public transit the rest.

In Minneapolis I commuted via bike for financial reasons so it was mostly a "suck it up, buttercup" sort of deal. You brought changes of clothes, outfitted your bike for the weather, and otherwise just made do. Honestly summer was worse than winter because I sweat a lot in heat. I cannot imagine living in that area without a car voluntarily. You just cut yourself off from far too much - but I suppose this was pre-Uber so the situation is a little bit more tenable.

Public transit in Minneapolis is basically for poor folks or those with DUIs - so it's not exactly stellar and usually not an option for most folks living in the metro area.

Edit: The follow up of "maybe 15 bad days" you had is for what most would call hardcore riders. The number of days the casual fair-weather bicycle commuter rides is far, far, less. I feel pretty comfortable saying this considering my family was known as crazies because we'd bike throughout the winter no matter the weather.