Hippolytus of Rome, writing in 204 AD in his commentary on the book of Daniel, states the ancient tradition of the dating of the birth of Christ as such:

"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."

Irenaeus of Lyon, who died around the year 200, held that Jesus was conceived in the womb of Mary on March 25th, basing this on the fact that Jesus died on Passover.

The association of the conception and death of Christ with Passover was fairly universal among the early Church Fathers, though calculations of the precise date of His birth ranged between December and January, due to the fact that the precise date of Passover varies from year to year. This tradition certainly is unrelated to any pagan festivals.

The actual celebration of the Nativity as a liturgical feast arose only later, with early accounts around the 4th century attesting to it across the Churches of both East and West. This likely leads to the misconception that the feast was dated so as to replace a pagan festival. In actuality, the dating is based on older traditions relating the birth of Christ to the date of Passover.