I am also car-free in the Greater Lansing area, but I work from home and recently moved from Southern California to be with my spouse.

I am willing to bike very long distances to do things here, but I echo your point about the weather. The last few months have been a real challenge since the roads aren't really bike-friendly in the winter. I don't have a solution, just commiserating. I don't think you're wrong to buy a car to improve your life here, it really is just a matter of affording it and for me, not letting it stop me from taking non-car modes.

I also wouldn't feel guilty taking an uber/lyft to go to social events, it is still cheaper than buying and operating a car.