Die Hard and Die Hard 2, taking place at Christmas, are definitely on the list for holiday viewing, and you can add Die Hard: With a Vengeance to the playlist, too. Sure, it takes place in the summer (presumably late summer, since school is in session), but it gives a nod to the Christmas setting of the first two movies in several scenes:
After he blows Bonwit Teller's Fifth Avenue store to bits, terrorist Simon Gruber (Jeremy Irons) forces Lt. John McClane (Bruce Willis) to walk the streets of Harlem wearing a racist placard. Shop owner Zeus Carver (Samuel L. Jackson) helps McClane and the pair have made it safely back to the station house when Gruber calls the head of Major Crimes:
Gruber: Where are my pigeons now?
Inspector Cobb: Pigeons?
Gruber: I had two pigeons, bright and gay, fly from me the other day. Why was it they did go? You cannot tell, you do not know.
Inspector Cobb: You mean McClane?
Gruber: No, I mean Santa Claus.
--Soon after, most of NYPD converges on the financial district after a subway explodes under Wall Street. McClane and Carver stop a kid stealing from a sidewalk vendor and have this exchange:
Kid #1: It's Christmas. You could steal City Hall.
McClane: Come on.
[Carver and McClane take the kids' bikes]
Kid #1: My bike?
McClane: Let's go. Come on.
Kid #1: That's my bike!
Carver: Yeah, it's Christmas!
--McClane: [to terrorists stopped in a tunnel] Hi, fellas. Mickey O'Brien, aqueduct security. Hey, listen, we got a report of a guy coming through here with, uh, eight reindeer.
[shoots the terrorists]
McClane: Yeah, they said he was a jolly, old, fat guy with a snowy, white beard. Cute little red and white suit. I'm surprised you didn't see him.
--[Bomb squad expert is defusing the bomb in Chester A. Arthur Elementary School]
Expert: Six booby traps, four dead ends, "and a Partridge in a pear tree." Okay, honey. Let's dance.
--There may be more, but these references should be enough to satisfy fans of the franchise. I haven't yet logged the Christmas connections in the fourth and fifth movies, having seen IV only six times and V only three, but will keep you posted! btw, although Willis has stated, "At the moment, I can run and I can fight on screen. But there will come a time when I no longer want to do that. That's when I’ll step away from the Die Hard films," a sixth installment is planned.