and that's fine. i generally don't think your airmasses need to be that cold to generate decent southern snowfall chances. obviously they still need to be supportive of snow but i don't think they need to be record-breaking per se. i think what you're purchasing with NAO blocking is a drunken storm track that gets easy to amplify, and by virtue of where that storm track ends up, it's easier to push colder air in as well.
the example i'll cite is the feb 12 2010 storm, which is, to this day, the most classic, no stress, southern slider i've ever seen. it happened on a friday night- that friday was cloudy with a high in the upper 30s in wilmington, cold for sure but nothing frigid. we got 4 inches of snow that night, arguably should of been more given the synoptics (jacksonville got 8). I think the night after radiational cooling brought it down to, say, 25? 23? Point is that one of the most slam dunk snow events that was working with a -nao i can remember was going into an airmass that was nothing to write home about. just my take.