I'm car-free in the sense that I don't have a car, but my parents do. I would be fine with just using my MTB that has tires with not very aggressive tread, rear rack with Wald folding baskets and fenders, but sometimes it's nice to go faster, so I have a road bike. I like my MTB, and want to to keep it in nice shape, so I just got a 3-speed to use in the winter.
I'd say it depends on your situation. A road bike would be fine for me in the summer, but with the way the streets are plowed in the winter, would be terrible to use.