I will always love "The Christmas Song (Chestnuts Roasting on an Open Fire) sung by Nat "King" Cole. It's the definition of classic "Christmas song" in my head. The title probably helps lol. I also love Bing Crosby's "White Christmas". I'm a sucker for the crooners xD
I am NOT a fan of all the autotuned junk that populates most radio stations this time of year, though. I can tolerate the novelty songs for a spell, but not if they are played over and over ("I Want a Hippopatmus for Christmas", etc.)
I do enjoy the religous carols as well (What? I'm Catholic! xD), and my favorite is a mash-up of "We Three Kings" and "Ukrainian Bell Carol (Carol of the Bells)" called "The Bell Carol of the Kings". Here's a recording of some high school singing it: https://www.youtube.com/watch?v=XY46C9Z5bY4
(not to be biased, but my church choir sound infinitely better, because they are back by the Northbrook brass Quintet, and also they are all adults
I also love the arrangement of "Go Tell It On The Mountain" that my church choir sings.