Christmas carols can be religious, and bring the meaning of Christmas into focus, or secular. There is nothing wrong with singing Frosty the Snowman, but it does not reach the theology of the season.
I am certain any list of Christmas carols will be meaningful only in a part of the world. I suspect each nation has its own, and respect that. In fact, adding what you sing in your part of the world in the comment section below is a way for us to all share knowledge.
In the United states I would suggest:
Joy to the world;
O Holy Night;
Hark the Herald Angels Sing;
O Little town of Bethlehem;
O Come All Ye Faithful;
Angels we Have Heard on High;
The First Noel;
It Came Upon the Midnight Clear;
and, We Three Kings.
Of course O Come, O Come Emanuel is ideal for Advent.
Silent Night has multiple versions. It was originally written by a priest in Austria. Unfortunately, it did not translate well as a song into English, so an Anglican bishop in Florida wrote new lyrics. Some people try to translate this back into German, but that is not what was originally written.
When I taught in a minor seminary, mathematics and chemistry, years ago there were five priests, and about six of us who were not priests, two faculty members (he English teacher and myself), a librarian, a secretary, and two grounds keepers. The five priests hosted a Christmas party, and one of them proclaimed it time to sing German Christmas carols. I had not realized they all had German names. It was an interesting experience, singing in the language in which many Christmas carols were originally written. And, they did have printed lyrics ready for the occasion.