8/25 Update. La Nina not looking so strong, with only 50% chance of happening now. That being said, I'm looking at the 83-84 season which featured a 2.0 Nino in Jan 83 to a -.7 Nina in Jan 84.
Here is an article, which admittedly goes over my head, which addresses that winter. I didn't find much in the way of how the NE winter went, but the overall theme was cold.http://journals.ametsoc.org/doi/pdf/10.1175/1520-0493(1984)112%3C1894%3ATCOTWS%3E2.0.CO%3B2
However this image is more clear, at least for the December record cold outbreak.
Bradley Airport snow fall for D,J,F,M was 7,14,1,19 with a major storm in March - snow north ice south. surprise March snowstorm for new england.
Central park snow for D,J,F,M was 2,11,1,2
So nothing really extreme in either location or in between. Could be a boring winter.
6/8 Some free time while eating lunch showed that the El Nino of 15/16 is over.
95-96 was the most brutal winter in my life with record 120+ inches of snow in Danbury. Due to the lack of a strong nino ahead of it, and my belief that Nina will be a little deeper, I'm going weigh that the least, thought its on the board. I'm also not going to go back much further in history due to the current global temps being so high. Temp dept was about -2.
98-98 BDL DJFM temp departures were +5, -.3, +2, +.6. Snow total was nearly 10" FOR THE SEASON.
2007-2008 DXR DJFM temps were -2, +2.7, -1.3, -1.4 with 27 inches of snow.
2010-2011 DXR DJFM temps were -5, -6, -3 and -1.6 with 75+" of snow.
So there are inconsistent La Nina winters. Sticking with last four weighing at 10%, 25%, 25% and 40% chronologically, the snowfalls are 12"+3"+7"+30" for a total 52" during DJFM. Temps shouldn't be long term brutal, but average 2-3 below normal.
Here is what the typical Jan-March looks like with La Nina