Do you walk to/from work in sneakers?
That said, some people in NYC have some seriously long walks to deal with (which they tackel at high speed), so I try not to be too judgemental about it. Dress shoes are made for walking, but walking shoes (sneakers) are WAY more comfortable, and can take abuse WAY more economically.
In bad weather, I also give everyone a pass if they're just trying to get from A to B. You have to be practical...
When it is absolutely pouring, or a blizzard, I will wear hiking boots with my raincoat and change at the office. Warning: Spoiler! (Click to show)
I have a pair of water-proof Rockports for this purpose (truly ghastly looking things, but I find over-shoes turn my actual shoes into sweaty pits of despair). I'll put my nice shoes in my briefcase or a bag, along with fresh socks, and change into them when I get to the office.
It is absolutely astonishing what a NYC snow storm can do to a pair of shoes. The combination of occasionally razor sharp ice, salt in various physical states, muddy sand, black oily slush and giant puddles of indeterminate depth make the perfect recipe for nice shoe destruction.
SWIMS. I keep one pair at my office, the other one at home.
When I get to work, I pull them off and place them somewhere discrete to dry out. Should I be going somewhere to a meeting or any other arrangement, I put a plastic bag into my satchel. When at location - take the SWIMS, put them in a bag and into the satchel. BOOM. Shoes are clean, everyone's happy.
Most of the times it's not the shoes I worry about - but the trousers. When it rains or snows sideways, SWIMS usually do a good job of protecting the shoes, while the trousers get most of the punishment.