Assalamualaikum. I grew up watching a lot of cartoons and I still really like them because to me, animation is like a fusion of storytelling and illustrating (2 of my favourite things). So, I remembered watching Barbie in A Christmas Carol and took a liking in Christmas songs; like Jingle Bells and We Wish You A Merry Christmas. I didn't know the songs' meaning that time, so I thought it was okay.
But, I found that I still like their melodies and listen to them occasionally although I already knew the meaning. So, is it forbidden to listen to Christmas songs? I’m not exactly sure what’s my intention, but I always see it as a childhood memory. But if it’s forbidden, I’ll try to stop. Thank you 😀
I can’t think of any explicit teaching in the Quran or Sunna that would forbid that. The Prophet 
did recommend at a few times not to engage in behaviors in which a Muslim copied non-Muslims for no good reason. I loved Charles Dickens’s A Christmas Carol and have no issue with reading it again myself. But I cannot really say if listening to Christmas songs is OK or not. I don’t mind it if they come on on the TV. But to actually seek them out to listen to them, I think it’s just a matter between you and God. It seems like an innocent enough pleasure to me, and I’m sure God is intelligent and sensitive enough to know that you mean no harm by it. But maybe don’t do it before other Muslims or tell them you do that since they may doubt your faith. And probably avoiding it altogether is the better choice just to avoid doing things that may be in a gray area.