I think what's going on regarding seasonal snow totals and the NAO is as the data set becomes larger the correlation begins to weaken and the correlation to -NAO and snow may not be what is was thought the past few decades...the same goes with ENSO phase.
Over the past decade or so we're learning a specific phase doesn't necessarily hold a correlation...I remember even in the mid-to-late 2000's the notion was that a weak La Nina meant big snows in New England...not necessarily the case. It's more about structure, placement, and short-scale changes within the oscillations. For example, you can have an overall long-term pattern which sucks...but within that overall pattern regime you can have periods where that relaxes and cards align and you can get slammed.
A lot of these connections are also established based on correlations to "major" or "significant" events...which leaves out alot of other data or samples.
This is why I hate how alot of indices are measured by a monthly...bi-monthly...or whatever average...this doesn't truly capture those very short-lived abrupt flips and it's those periods which are going to produce some type of weather.