It's been a long time since I've seen it, how integral is Christmas to the actual plot of the movie? Could it take place in another time of year and everything would proceed the same way? A Christmas movie needs more than just a bit of scenery here and there. It's why Die Hard is not a Christmas movie.
Well as James points out 2 of the big scenes involve the Christmas tree lighting. So the plot needs that plot point to keep the movie moving along.
Christmas is ever present in the movie, as it takes place during Christmas, missle toe is important, and Alfred/Bruce wish each other Merry Christmas a few times. I mean Home Alone could of taken place of labor day too.
Now keep in mind this was directed by Burton, and how much of a non Batman movie it really is. And if Burton was going to make a Christmas movie, this is probably would it would look like. A bit of a dark gothic tale.
If you took out the Christmas element it wouldn't really be the same movie, and a lot of the themes dealing with Penguin/Batman/Catwomen and their place in the world does fit into a Christmas theme about family and loneliness.
Max Schreck is a perfect scrooge like character as well as James points out.
So overall I think that Christmas is more intergral to the movie than Batman is. Replace the Batman characters with generic characters and the movie loses less than if you took Christmas out of it. at least IMO.
Like I said in my OP, if Burton was going to make a Xmas movie this is what I would picture. He isn't going to remake its a wonderful life and be all schmaltzy. 90's Burton would of done exactly this type of dark gothic tale. He just was able to use the Batman license to tell his Christmas story.