Northern Parulas are not regular winter residents in New Jersey. In fact, most of them are gone by mid-October, with only a few lingering into November. Like other warblers, Northern Parulas are primarily insectivorous, which makes it difficult for them to survive a cold winter at northerly latitudes. While they breed throughout eastern North America, they spend their winters in the Caribbean or Mexico and Central America. This warbler should be well south of here by now.
The greenish head and green-tinged flight feathers mark it as a first-winter bird, and the lack of any orange or red markings around the neck suggest that it is a female. (I am not sure whether that character is reliable for sexing first-year birds.) One detail I had not noticed initially but saw in the photos is the yellow wash on the flanks. Not all field guides show this marking.
I probably ended up with more photos of this part of the bird than any other.