Yes, you are right on this point, how Jesus wasn't born on December 25!
I know a family who do NOTHING on Christmas day - no tree, no presents, I don't know if they even fix a nice meal or what.
Although on principle I think it would be good to NOT celebrate on December 25 because of its pagan associations, in practice it just seems harsh! I agree it is good to make that known in the family, clear and understood, and yet some celebration on December 25 does not seem inappropriate in this day and age. Remembering Jesus' birthday, fellowshipping with family and friends, sharing goodwill, these things are acceptable any time of year. Who wants to be sitting around in a cold, dark house, doing mundane things when everyone else is celebrating?