Die Hard has become the pre-eminent example here, but there are plenty of others*.
Things to Come – H.G. Wells himself wrote the screenplay for this weirdly uneven bit of prediction made in 1937. He starts it out in a city clumsily called “Everytown”, but which is clearly London, with a conspicuous St. Paul’s cathedral dome in it. It’s Christmas time, with plenty of shots of holly, Father Christmas, Christmas Geese hanging in the shop window, and carolers, but it’s only an excuse to offer, side by side with that, plenty of warnings about an impending war. (The enemy is not named or implied, but you’d have to be tone-deaf not to realize it was Germany). The contrast between Peace of Earth and Imminent War is obviously what Wells was after, and he depicts a rapidly-evolving war with prescient scenes of London being bombed from the air and large parts being reduced to rubble.
On Her Majesty’s Secret Service – A lot of Bond films got released around Christmas (unless they were released for the Summer Season), but I don’t know of any others that exploited the Christmas setting like this. It even has a Christmas song in it – “Do you know how Christmas Trees are Grown?”, written by John Barry with lyrics by Hal David (!!), and sung by Nina. There’s a Christmas tree in Blofeld’s headquarters, and there are Christmas Presents Which feature as a plot point) If you wanted an action-adventure movie to serve as a “Christmas movie”, OHMSS has a better claim to it that Die Hard – Christmas is baked in its DNA as in a Christmas cookie.
The Apartment – Billy Wilder’s dramedy with Jack Lemmon, Shirley MacLaine, and Fred MacMurray as The Bad Guy is set in NYC at Christmas.
Batman Returns – Tim Burton’s second Batman film is set in Gotham City at Christmas, looking like Rockefeller Center in New York, and even has a scene in front of the giant Christmas Tree clearly intended to be the one over the real city’s skating rink.
The Thin Man – I’d forgotten that this one was set at Christmas, but it suffuses the film.
Any others? Here’s a list of some – 16 Great Christmas Movies That Aren’t Christmas Movies
*to the point where there’s a Fake Little Golden Book version of it.
There’s one for Home Alone, too, but that one has a legit claim on being a “Christmas movie”