The print depicts a lady in masquerade dress, with clothing arranged in a manner suggestive of a nun, without being a full "costume." Masquerade costumes were often like that--items or details suggested a character or concept, but they did not necessarily have to be a full, authentic costume. And in this case--a lovely young lady who wanted to show her best features--an authentic habit would interfere with that goal.
Then, as now (doesn't every costume party have at least one naughty nun?), the nun costume was a bit tongue in cheek--the print's inscription reads:
On her white breast a sparkling cross she wore
Which Jews might kiss and Infidels adore
Political incorrectness aside, it's a humourous jab at the real object of men's attention at this particular example of piety.
And why does it make me think of New Year's? Well, there's always the opportunity for costume parties as New Year's Eve fetes (though I've encountered most naughty nuns at Halloween bashes). But in all honesty, I found the image of the stiff old mask dropping away and the young face beneath revealed to be rather symbolic of embarking on a new year. In hopes we can pull away a bit more artifice and illusion and get deeper at the core of living this year.