We do not know when Christ was born. It could be December 25th, so relax, Merry Christmas.
The scriptures do not tell us. Recitation of the date in a conventional format is a sign that God uses conventions to communicate with us, nothing more.*
Christmas is not necessarily a pagan holiday in origin.
Neither is it necessarily based on a real tradition of when he was born.
Roll with it.
*As far as I can discover, every LDS source for the April 6 date ultimately traces itself to poetic reformulation of the ‘year of our Lord’ dating formula in the Doctrine and Covenants. If anyone knows of some other source, I would be happy to hear it.