I have what I believe to be the correct answer to the "is Die Hard a Christmas movie" question. The answer is yes, it's a Tier 3 Christmas movie.
Tier 1 are movies about canon Christmas characters or Christmas itself.
- Elf
- Miracle on 34th Street
- A Christmas Carol
- How the Grinch Stole Christmas
Tier 2 are movies about regular people but the plot revolves around Christmas. The movie wouldn't work without the Christmas element.
- A Christmas Story
- National Lampoon's Christmas Vacation
- Home Alone
- Bad Santa
Tier 3 are movies that are set during Christmas, but the plot doesn't depend on it. The movie would still work if it wasn't set at Christmas.
- Die Hard
- Batman Returns
- Kiss Kiss Bang Bang
- Carol