If the suggestion were correct, one would expect to find at least a single reference by early Christians to support it. Instead we find scores of quotations from Church Fathers indicating a desire to distance themselves from pagan religions.
Although the date of Christ’s birth is not given to us in Scripture, there is documented evidence that December 25 was already of some significance to Christians prior to A.D. 354. One example can be found in the writings of Hyppolytus of Rome, who explains in his Commentary on the book of Daniel (c. A.D. 204) that the Lord’s birth was believed to have occurred on that day:
For the first advent of our Lord in the flesh, when he was born in Bethlehem, was December 25th, Wednesday, while Augustus was in his forty-second year, but from Adam, five thousand and five hundred years. He suffered in the thirty-third year, March 25th, Friday, the eighteenth year of Tiberius Caesar, while Rufus and Roubellion were Consuls.
That still does not explain why anyone would be tending flocks in the fields at night when temperatures would drop below freezing. Even today shepherds do not do that. Why would they do such a thing in the first century? Something does not jibe with the facts of the real facts of life.
On the other hand, it would explain why it would be VERY necessary to find room at the Inn... when any other time one could sleep outside with not too much discomfort.