NYC has winters, and I never even thought of driving in Manhattan.
There are many ways to make a city walkable in winters, but for the most part, density suffices: the city acts as a shield and a heater.
As for having public transport at the edges of the city only - not a problem if that boundary is never too far.
For some part, Moscow has embraced this idea, with the so-called transportation "rings" (highways and subway) encircling the city - but they do branch inwards.
