I would have to guess that checking the weather in the morning is a ritual of almost every New Yorker. Especially in these in between seasons when it can be 30 degrees and slushy one day and 65 and sunny the following. In the winter months, I almost always wear a pair of boots to work and change into flats when I get there. The shoes I want to wear all day at work are rarely what I need to wear out in the elements.
Rain is the absolute worst in the city, I would rather take snow any day. Soggy feet=biggest pet peeve. But since we don't have the option of heading out to our car parked in our garage and then parking as close as we can in the next parking lot, we need to be even more prepared that the average commuter. If you are armed with all of the essentials: rain jacket, rain boots and umbrella, the situation can be more manageable.
The Chelsea rain boots from J.Crew have become my go-to over the past few years. I always leave one pair at work just in case the forecast didn't originally call for rain but down the showers pour! They are comfortable, easy to get on and off with the tab on the back and best of all, if you are too busy and forget to change out of them once you get to work they can be easily pass for a pair of cute regular booties. They don't have many colors left this season, but I'm sure they will bring them back as they have year after year.
I also own a pair of tall & short Hunters but find myself reaching for them less and less during the rain. The short Hunters are still great for dog walking, when you want to just slip in and out without having to bend over, but I also find that they can be very clunky. My tall Hunters are the best on slushy, snowy days in the city. You can walk straight on through those disastrous curbside black holes without any issues. The added fleece lined socks made them as warm and cozy.
When the snow hasn't quite turned to slush yet (which it will...and it will be gross), my Sorel's are the best for maneuvering the streets. These boots are very heavy and take a bit of time to get used to but they have excellent traction and keep your toes extra dry and warm. My Bean Boots are also a staple in the snow with a thick sock.
Last but not least, and the most debatable choice, my Uggs. I have been a loyal Ugg owner since my high schools days when they first became popular in the US. I remember spending hours scouring eBay and bidding on every pair of Nude/Short/Size 8 I could find. Nowadays, I have learned that you can't wear them in any kind of elements aside from just plain-old cold. They won't hold up in any sort of wetness or exposure to salt but if it's just a cold, dry day. I'd say from November-March, I wear my minis in black almost every day to walk the dogs. They're easy to slide on and feel like you're weather your slippers outside. Fashionable? No, but if you only saw the outfits I wear outside for walking the dogs, these would be considered just fine.