Around the time I traveled (March), it was still pretty chilly with some sun. Toward the end of the trip it started to get really cold. Since I checked the weather and expected this, I was prepared when I was packing.
If you are traveling to New York during spring time, most likely it'll still have its days of chilly weather. One thing you must keep in mind is the WIND.
So from my experience, what I wore almost all the time was:
- coat
- thinner jacket (for layering)
- comfy shoes
- scarf
