The goal of most "anti-car" (most aren't really anti-car, just anti-cars in the city) people is not just to create pedestrian zones, but also to change land-use patterns so that it doesn't feel as necessary to drive everywhere.

This is absolutely implementation-specific. American cities tried similar transit/pedestrian malls but failed. It is my belief that with good governance and infrastructure, cities can adapt to a car-free lifestyle, even in places with extreme winter.

For example, in snowy and hilly Montreal an entire underground shopping mall exists, (https://en.wikipedia.org/wiki/Underground_City,_Montreal) allowing for transit commuters to walk around (or rather, under) the city center comfortably even in the dead of winter. Even if those commuters took their cars into the office that day, they still benefit from this infrastructure, because it potentially reduces the need for additional car trips (if you're just grabbing a quick bite to eat or a few groceries).