From the Department of Sanitation/311:
In order to ensure that all city streets are plowed and salted throughout the current blizzard, the Department of Sanitation has announced that all scheduled refuse and recycling pickups will be suspended citywide. Announcements will be made when curbside pickups will resume. For any Sanitation related questions on the most up-to-date information, residents can call 3-1-1 or visit www.nyc.gov/sanitation.
In short - don't put your trash out unless you don't care about your neighbors who will have to meet the New Year looking at it.