I am traveling from the UK to USA for a few months, my first stop being New York City for a few weeks over Christmas and New Years.
Generally speaking, what is the weather like? What would be appropriate clothing? I think it snows often, so I was assuming some waterproof shoes / boots would be sensible at least.
Winter weather on the northeast US coast is a battle between cold, dry air blowing in from the northwest, and (relatively) warm, humid air from the Gulf Stream coming up from the Caribbean. The weather is determined by which of those two forces is “winning” at a given moment, and it can swing abruptly when the balance shifts.
Expect cold, windy, rainy weather. But don’t be surprised to get snow and ice if those Canadians send a strong cold front.
The comment comparing New York to Scotland is a good one. Dress like you are going to Aberdeen and you should be just fine in New York.