A reader writes in asking, "I've been looking for some songs I can sing to the gods of my tradition at the winter holidays. I saw a few Christmas carols where someone had substituted "Goddess" for references to God and Jesus. Would these be good Pagan songs to sing at my Yule ceremony?"
You can sing anything you like. However, changing words from Christian to Pagan gods isn't a "Pagan song." It's a Christian song with Pagan substitutions. If you look at the lyrics of most Christmas carols -- at least the spiritual ones -- they're spiritual all the way through, not just because a word refers to God or Jesus. The entire content of the song is Christian in nature -- which is fine, because it's designed to celebrate a Christian holiday. On the flip side, if someone has rewritten the lyrics completely to reflect a Pagan theme with the same music, then that's a slightly different situation.
There are a couple of things you can do instead. The most obvious would be to write your own song. If there's a particular deity you wish to honor, write a song. It doesn't have to be fancy or complex -- it doesn't even have to rhyme. It just has to be from the heart. Instead of plugging Mars or Apollo or Cernunnos into Silent Night, write a song that honors the gods of your tradition in their own cultural and religious context. You could sing about themes such as rebirth, the nights growing shorter, the return of the sun, the coldness of the earth, or any of the your own deities.
Another option would be to look for specifically Pagan music. There are a number of Pagan and Wiccan musicians who do have songs available honoring different deities and celebrating the Yule season. The band Emerald Rose has an absolutely hilarious (and instantly sing-along-able) tune called Santa Claus is Pagan Too. A quick Internet search ought to help you find some good Pagan music resources.
Finally, you may wish to look for songs that are secular but that still reflect values and themes that represent your Pagan beliefs. Traditional English folksongs such as The Wassail Song might be more your speed, or even Greensleeves, which was originally written during the Elizabethan era as a love song.