I live in a city (Seattle) and walk to the grocery store. I usually only buy one bag of groceries at a time. The grocery store is less than a 5 minute walk, so I don't need to make big trips and can make small trips often.
Similar to another poster, I live in Boston. We get a bit more than a meter (~41 inches I think) every year on average. Last year we got slammed with nearly 3 meters (about 9 feet) of snow.
Groceries? I walk. Have one option a 15-minute walk away, and two 25-minute walks away. I do 3 to 4 bags at a time, not a problem. I also have subway/bus literally across the street, and right next to highway for when driving to clients makes sense -- but usually can get to them via mass transit (subway and bus) so long as they're in certain areas within about 20 miles (32km) from where I live.
Still own a car, but it's only for fun, not necessity and I never use it for errands. If it wasn't for fun, I'd not bother with owning one.
not saying the parent poster's solution would 100% work, but as an anecdote:
I live in Boston. It snows here and I do often buy more than one bag of groceries at a time. Fortunately, I just walk two blocks down the street and go into one of the two grocery stores that are right there.
Compare where I grew up in southern NH: it snows there, too, but the nearest grocery store was a 20 minute drive, so of course I would drive there. Rural NH is not a city, though.
Snow is even more of a reason to get rid of cars. A car-less city with underground subways/metros and integrated residential/light commercial districts sounds like a dream. No more shovelling, no more plows, no more going outside during the cold wind! I would love to be able to go from my house to the grocery store and work and the movie theatre (or whatever else) without ever having to set foot outside. This is possible for some people in Toronto and a few other big cities (that I know of) but not the common case.
Remember downtown Minneapolis being like that for obvious reasons. I think a lot of people in the Minneapolis area have heated garages so essentially you can park in a garage downtown, walk around the skywalks between the downtown skyscrapers, and never have to set outside.
I was only there for the Superbowl and never actually walked one, so maybe it's not so convenient.
I think it's easy to lose perspective of these luxuries that we now see as commodities. We've been marketed to that cars are status symbols of wealth, and that not owning a car means you're somehow a deviant, or too poor to own one - both of which are seen in a negative light.
The problem is that personal car ownership with our current technology does not scale up, when taking into account of environmental impact. Nor when you reflect on just how much public right of way we've given up to infrastructure for cars. Nor when you think of how many people die of automobile accidents. Nor or the impact cars have on living in social communities.