I think the idea of an old city going car free is unlikely. However, I could see a new car-free city popping up in a snow-free zone. There is a large community called "The Villages" near me where a good chunk of the transportation takes place by golf cart, but it was designed to allow this.

A community designed for car-free transportation could attract a certain breed who want to save the planet and/or save cash. I just don't see how you could retro fit older large cities where people are already committed to long commutes and going big distances for shopping or entertainment.