I recall Cowboy Bill Flett, MacLeish's 'stache, et al but IIRC, those were permanent fixtures rather than something to do for the playoffs.
Not that this article is the defining word but it goes into the beards a bit:
Likewise, growing a beard for the Stanley Cup playoffs didn't come into vogue until about 1980, when the New York Islanders began their run of four straight championships.
That, at least, is the consensus of several National Hockey League veterans who were asked to track the origin of the tradition.
``I'm pretty sure we started that because the Canadiens won the four Cups before that and [Canadiens President Sam Pollock] had a rule that [prohibited] their players from wearing beards,'' former Islanders assistant general manager Jim Devellano said. ``We didn't care if they wore a beard or wore their hair down to their [rear ends]. So we had a bunch of guys with beards.''