How was the day of Christmas allocated ?

M'Clintock and Strong's Cyclopeodia says the day of Christs birth cannot be ascertained from the Bible, or indeed from any other source. Vol. II, p. 276 Luke 2:2-11 shows that the shepherds were in the fields at night at the time of Jesus' birth. The book 'Daily life in the time of Jesus' states: "The flocks...passed the winter under cover; and from this alone it may be seen that the traditional date for Christmas, in the winter, is unlikely to be right, since the Gospel says that the shepherds were in the fields." Henri Daniel-Rops, p. 228 The Encyclopedia Americana informs us that the reason for establishing December 25 as Christmas was to correspond to pagan festivals that took place around the time of the winter solstice, when the days began to lengthen, to celebrate the rebirth of the sun. Vol. 6 p. 666. The New Catholic Encyclopedia acknowledges: "The date of the Christ's birth is not known. The Gospels indicate neither the day or the month...According to the hypothesis suggested by H. Usener...and accepted by most scholars today, the birth of Christ was assigned the date of the winter solstice(December 25 in the Julian calendar, January 6 in the Egyptian), because on this day the pagan devotees of Mithra celebrated the birthday of the invincible sun." Vol. III, p. 656.