Being the heathen I am I love quite a few alternative christmas songs. Depends what you mean by unconventional, though. If you mean still Christmas but different than baby boomer Christmas songs, then there’s
Atheist Christmas Carol by Vienna Teng (heathen!)
Love is Christmas by Sara Barielles
And a little sad but still gorgeous, River originally by Joni Mitchell, though I prefer the linked version by Barielles.
Now, there’s also ‘unconventional’ as in not really about Christmas at all, but about the season, in which case I also have to add
Winter Song by Bareilles and Ingrid Michelson
Fun fact, another of my favorites is the Carol of the Bells, which is considered ‘traditional’, but is actually ancient. Pre-history ancient, it’s originally from Ukraine, and existed as a magical chant to bring in the new year (celebrated in April, not January) before the introduction of Christianity. Pretty cool. And makes some pretty great metal.