Was Jesus really born on December 25th?

I mean...it gets down into the 50 F temperature range in that part of the world in late December.

Do we really buy that the shepherds were laying watch over their flocks at night like Luke described in 2:8

or

do we think that the Roman hegemons wanted to centralize authority, hijacked the paleo-Christian movement, fabricated Christian holidays, and placed them on the calendar in such a way as to directly compete with existing "pagan" holidays like equinoxes (Easter), solstices (midsummer, Saturnalia), Lemuria (originally targeted by All Saints Day which was later moved by Pope Gregory), and Samhain (aka Halloween, now targeted by All Saints Day)?