I think it is common knowledge that Jesus likely was not born on December 25.

He may have been, but no one has a written record of the exact day of Jesus' birth. It is helpful to know what we do know.

That a star was seen so there must have been a clear enough sky.

that shepherds were in the field so it must have been warm enough for people to be outside.

That Mary the mother of Jesus was traveling to Bethlehem because of a known proclamation to pay taxes to Rome

so we do know the season.