I guess temperature is really variable, because I wouldn't call weather in NYC now or next week "very cold." It is seasonal. Lows at nights in the 20s and highs in the mid-30s. Although it is true, with the wind rushing down the streets it can feel much colder....The true bitter cold usually comes in at the end of January and lasts through February.
Again, everything depends upon your point of view. My California cousin breaks out the winter coats when the temperature drops to 50.
This time of year, I wear my regular wool winter coat. It is knee-length and I wear knee high boots. I find that combination keeps me the most comfortable. The parts to keep warm are your ears, head, fingers, toes, and torso.
Also keep in mind that layers are fantastic, because the minute you step indoors you will need to rip off half your clothing so you don't pass out from the heat. It is for this reason that I don't like long underwear. They are extraordinarily difficult to remove in public places.
IF it snows, you will need tall boots because there are invisible puddles everywhere. Like, you step onto what looks like pavement and suddenly you are knee-high in an ice bath.
I think your capsule runs on the casual side, but that depends upon what you like to do.
If you go to Bloomingdales stop first at the concierge on the first floor and get a visitor's pass, which will alert the cashiers to NOT charge you sales tax. Nice, huh?
If you like music, I urge you to go to Carnegie Hall. The acoustics there make the music sound like it inhabits your soul and bursts outwards...no matter where you sit. It is incredible.
Have fun.