That was a cold and solid winter for here. December 1983 had a couple good SW flow events that gave some good snow followed by those brutal arctic outbreaks. February 1984 was a dud though...it was an absolute torch with little snow. December, January, and March were very wintry months that season though.
The storm you are thinking of is the March 28-29, 1984 storm. It gave 17.6" of snow here. Extremely dynamic storm with a lot of thundersnow in the Boston suburbs and wind gusts over hurricane force. (Blue Hill had a gust over 100mph) Perfect way to end a winter.