Where were you living exactly?
December 1981 is the 5th snowiest on record dating back to 1956 for my area north of Boston.
Logan airport had very healthy snows...17.6" for the month with about a 1' on 12/6.
It does look as though there was a rather steep gradient, as Central Park had a meager 2.1". This is also consistent with my expectation...not necessarily that extreme of a gradient, though. Dec 1981 reminds me of Dec 2007 with that sharp cutoff.