Christmas carols that don't mention Christmas
Do You Hear What I Hear
The First Noel
Frosty the Snowman
Hark the Herald Angels Sing
Jingle Bells
Little Drummer Boy
Do You Hear What I Hear
The First Noel
Frosty the Snowman
Hark the Herald Angels Sing
Jingle Bells
Little Drummer Boy
winter wonderland
shareJingle Bells. I think.
shareJoy to the World
shareSilent Night
shareNoel means Christmas. The First Noel literally means the first Christmas.
Frosty the Snowman isn't a Christmas Carol. Neither is Jingle Bells. They are winter songs.
I Saw Mommy Kissing Santa Claus
shareAvoiding religion?
shareDo you mean songs that are strictly secular? Some of the ones you mention, like "Do You Hear What I Hear?" or "The First Noël" do not specifically use the word "Christmas," but are about the birth of Christ.
"Jingle Bells" was originally intended to refer to Thanksgiving:
https://en.wikipedia.org/wiki/Jingle_Bells
Some other songs that are about winter, but are associated with Christmas, include:
"A Marshmallow World"
"Baby, It's Cold Outside"
"Let It Snow"
"Sleigh Ride"
"Suzy Snowflake"
There are other compositions such as the "Linus and Lucy" theme that some associate with the holiday because it was used in A Charlie Brown Christmas.
https://www.youtube.com/watch?v=x6zypc_LhnM