Definitely. Any song that refers simply to “Christmas” isn’t a Christmas song in my book.
Because I am the son of a WW2 vet, I am a sucker for WW2 era songs like White Christmas and the epically sad Have Yourself A Merry Little Christmas because of their stories. Growing up a huge Presbyterian church, I also love Organ and Choir songs. St Martin in the Fields, Mormon Tabernacle, Prague Philharmonic, Choir of Kings College, etc.