The James Barke edition of "The Complete Poems and Songs of Robert Burns" only contains "Masonic Song" as posted by Peace, and the index of first lines has nothing resembling "It happened on a winter's night.... ".

I have numerous Masonic books in my collection but none of the songbooks contains the song you are looking for. It may be a song about Masons rather than of Masons, if you see what I mean!

I'm intrigued, so will continue research.

Alan