There was a festival at the time of the mid winter solstice long before the Christians stole the festival.
The birth of christ was celebrated in several months, the most common being March (28th)
Christianity was failing so the celebrations were moved to coincide wiith those of the Pagan Sun King. (At the conference of Popes at Nicea, 2nd or 5th century, sorryI've forgot the dates, 2nd I think, about 339)
The Sun King died on the shortest day (winter solstice)
A few days later when the observers could see the day lengthening he was reborn (25/12)
12 days later he was armed and named (The Epiphany)
On 25/03 ( Lady Day) he impregnates his mother the earth so he can be reborn 9 months later ( 25/12)
We can have the mid winter festival without Christ (I celebrate it every year) but we can't have the Mass of Christ without the Christian figure head, from whence the festival was named.