My little quest started when I read a NY Times Op Ed. There are a number of these songs, it turns out, and other bloggers and writers have done the research for me: I thank them, including the wonderful people at Mental Floss and this article. (a must read).
Some may argue that these are NOT Christmas songs, but rather songs about what I would now call the "secular Christmas". True, these are not hymns. But it is true that the American celebration of Christmas incorporates many aspects of non-religious symbolism - this ground has been covered by other writers.
I consider them Christmas songs. I think, in particular, few would argue that "I'll be Home for Christmas" isn't one of the most heartfelt Christmas songs every written.
(Note, I have not done any of this research myself from original sources, just from Internet articles. I am not a musician or a music expert, just someone who likes to listen to well written music. So if I end up spreading wrong information, I apologize. I did try more than one source, but - as you well know- you can't trust everything you read on the Internet.)
1. White Christmas: Irving Berlin lived to 101, married a Catholic woman back when that type of intermarriage was extremely scandalous (to both families) and defined Christmas for entire generations of American Christians. (Incidentally, he also wrote "Easter Parade" and "God Bless America".) The next time you wonder if you will be having a white Christmas, and if you can't figure out exactly why that should be so important, blame Bing Crosby and Irving Berlin.
2. Silver Bells: this one is another movie song, and talks about the bells of the Salvation Army "in the city". (I always assume it is New York City.)
3. Winter Wonderland: the author of this song was a Jewish man from Brooklyn. The air must have been a lot less polluted in those days. When I grew up in New York City in the 1950's and early 1960's, a snowy day was more like a Black Crusted Snow Wasteland.
4. The Christmas Song (Chestnuts Roasting on an Open Fire): The Nat King Cole version is one of my favorite songs ever. This brings back so many memories of the holiday season in the late 60's in midtown Manhattan and the vendors who would sell roasted chestnuts. The fragrance carried for blocks.
Jack Frost would certainly nip at your nose in NYC. The climate there is so damp, it feels way colder than it really is.
5. Let it Snow, Let it Snow, Let it Snow: the duo, both Jewish, who wrote that song, also wrote "The Christmas Waltz".
6. I'll be Home for Christmas. As an almost-history major in college, this song makes me think of my aunts and uncles during World War II.
And last but not least, something I picked up in my research: Rudolph the Red Nosed Reindeer. It would seem that Johnny Marks, the author of that song (and also "Rockin' Round the Christmas Tree" and "A Holly Jolly Christmas") was Jewish.