(Not making light of anyones celebrations, just making note, how intertwined Christmas has become in many different traditions. Norse. Germanic. Roman. Dunno what else off the top of my head. Most of which have nothing to do with the birth of the baby Jesus, which many think happened in September, not December.)
As I understand it, it's the other way around. Christians co-opted and incorporated existing celebrations into Jesus birthday funtimes.
Hil, I'm sorry you feel uncomfortable. I guess with all the mice business, you're probably not inclined to make a deal of this. Are you lighting a menorah (just curious)?
Religious and holiday stuff can pretty fraught. I grew up treating Hanukkah and Christmas pretty casually, being in an interfaith home (Methodist and Reform). But D didn't celebrate Hanukkah at all when very young, and while he and his family were Lubavitcher it meant passing out menorahs to other Jews. And now he's basically atheist (I think). So I'm all like, LATKES WHEE! and he's all like, sure I'll eat some potato pancakes.
Also, weirdly, my mother kind of believes there's a war on Christmas. I'm like, you have been married to a Jew for over forty years - WTH?