The last act of Ghostbusters 2 takes place on New Year’s Eve, and apparently NYC has already taken down all of its Christmas decorations already. (New Year’s Eve is instrumental to the plot, on the other hand).
Just a little ironic. 
I would say many of the Harry Potter movies would meet the OP’s criteria. Christmas break is often referenced, but not really essential to the plot.
By that standard, there are probably passing references to Christmas in numerous boarding-school-based films, like Tom Brown’s School Days in its various adaptations.
The 1980 film Breaking Glass with Hazel O’Conner had the singer and her manager spending Christmas on a train in a yard, stopped due to a strike.
As has become my personal annual tradition I have resurrected my “Is Die Hard a Christmas Movie?” thread here in case anyone wants to discuss that movie in particular.
The movie “The Silent Partner” begins with a robbery by a mall Santa, but the rest of the movie is basically unrelated to Christmas.
Watching the MST3K 5th season fan favorite ‘Mitchell’ (with Joe Don Baker as the title police detective) recently, it fits this OP. It takes place in Southern California so the weather’s balmy (there’s a few pool side lounging scenes), and at least in the MST3K edit there’s only two displays of Christmas - a string of Christmas cards in the police station, and a Christmas tree with many presents under it in the background as the criminal Deany (John Saxon) tries to bribe Mitchell. While J&tBs do point out he gets a lot of presents for a criminal, this is not relevant to the plot.
Well, as a technical dodge, DH2 is also book-ended around Christmas, with the movie starting out with McClane getting a parking ticket at the airport and ending with…
Parking control manager: Hey, McClain. Y’know that ticket you got? [Tears up the ticket and throws it like confetti] What the hell, it’s Christmas![COLOR=Black] {season*}
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But the actual story and plot events don’t rely on Christmas per se. It could be just any super-busy winter day at any airport. [e.g. “What the hell, it’s Valentines Day!” and we love you for what you just did.]
And, in fact, I thought it was a bit odd that, when the bad guys visit the tiny church abutting the airport’s property, it wasn’t lavishly decorated for – well, THE most important event for such a church to commemorate.
–G!
*The weather conditions are important, though.
I’m a huge movie fan, and this is an interesting topic for a thread. I.e., listing films that take place around the holidays, but aren’t purely Christmas-themed films like A Christmas Carol, Surviving Christmas, A Christmas Story, etc.
Here are some of my picks:
Blast of Silence (1961): Disturbing & well-done neo-noir film that follows a hit man who is hired to perform a “job” in NYC; it coincidentally takes place right before - or during - the Christmas holidays. Though you do see holiday decorations & the winter setting is obvious, Christmas isn’t referenced to a great extent.
Three Days of the Condor (1975): Great espionage thriller starring Robert Redford. Takes place partially in NYC during the holidays, though that is merely incidental.
The Conversation (1974): Superb thriller starring Gene Hackman as a wire-tapper in the SF Bay area. Coincidentally takes place in early December.
Easter is way more important. Perhaps to many people that don’t think about it much, they are equivalent, but Christianity is way more based around what supposedly happened at Easter.
The Impossible takes place around Christmas, but that’s merely coincidental to the date of the Indian Ocean tsunami (Dec. 26th, 2004).
The Apartment. The movie’s climax is at Christmas, but it’s used to show just how big a dick the Fred McMurray character is.
The Thin Man takes place around Christmas, and there are even gifts given, but the entire plot involves a mystery that has nothing to do with the holiday (other than as an excuse to gather the suspects together at the end). Note that After the Thin Man is one of the few New Year’s Eve movies.