MMario, Mrrzy, lots of songs are 'tradtional' in the sense that you mean.  (Though I'd wager most folks who know the words to "I Heard The Bells..." have learned them via recordings or hymnals, whereas they learned "Jingle Bells" aurally.)

We do modify the words to old songs (e.g., singing "brothers" instead of "darkies" in Stephen Foster's "Old Folks At Home."  But I personally don't like it when a known composer's poem is re-written in a way that radically changes the meaning.  (What my fellow Unitarians have done with "O Little Town Of Bethlehem," for instance, I find just silly.)

At any rate, I'm no purist and have altered lines here and there myself (not always intentionally), so if you want to rewrite old carols, go ahead, and enjoy the singing.

Just wanted to make a distinction between songs such as Silent Night (Stille Nacht) which were formally written down and songs that have been disseminated through oral/aural tradition.  Nobody really knows what the original words to "Go Tell It On The Mountain," do they?  We do know the original words to Longfellow's poem.    Click here.
The familiar song omits two verses and changes the order of the others.  I just hope that if folks start making more changes, we won't forget the original poetry.

Genie