Yes, Jesus was born on Dec 25!

[WinnieW]

Christians don't know what year he was born in, nevermind what day.

That's true.

The birthday of Jesus was chosen by the Catholic curch, but that's a long story to tell. Mankind don't know either the exact date or year of the birthday of Jesus.
And there was a calender reform in 1582 (from Julian calender to Gregorian calender).

And having a christmas tree isn't a religious rite, it's a traditional event.

Long before Europe was invaded by Christians, the Germanic peoples celebrated winter solstice in honour of Odin - the Pagan God of wisdom, around the same date as Christmas.

This is correct.