It's not actually a Christmas song. No mention of Christ or Christmas in it.
The composer, Felix Bernhard, was at least born Jewish, with a Yiddish-speaking mother. So feel free to sing it all you want.
The lyricist, Richard B. Smith, was in a sanatorium with tuberculosis when he wrote the words, and died young a few years later. So remember it's not entirely a happy song if you do sing it.
The alternative words were written for children to sing in 1953, and it looks like some later revisions kept the "circus clown" but took out the "kids" or "kiddies."
I think most of the lyricists and composers of great American Christmas songs were Jewish.