Looking at New York as a whole, I would say probably not, but specific regions, I am sure there has been winters that have generated very little or no snow. This year it is does to a very strong La Nina year. La Nina is characterized by warmer temperatures and lower levels of moisture. Here is NOAA's page on this weather pattern as well as wikipedia's.
http://www.elnino.noaa.gov/lanina.html
http://en.wikipedia.org/wiki/La_Ni%C3%B1…
http://www.elnino.noaa.gov/lanina.html
http://en.wikipedia.org/wiki/La_Ni%C3%B1…
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Yes i believe this winter.....