The word for Christmas in late Old English is Cristes Maesse, the Mass of Christ, first found in 1038 (newadvent.org) The present calendar is predicated on Jesus birth being Dec. 25th and his circumcision/ presentation in the Temple 8 days later falling on January 1st, which begins the anno dominus. This lines up with the early celebration of Christmas on Dec. 25th.
Birth of Christ at first not celebrated.
“Christmas was not among the earliest festivals of the Church. Irenaeus and Tertullian omit it from their lists of feasts; Origen, glancing perhaps at the discreditable imperial Natalitia, asserts (in Lev. Hom. viii in Migne, P.G., XII, 495) that in the Scriptures sinners alone, not saints, celebrate their birthday” (newadvent.org)
Then combined with Epiphany on January 6th, which is the celebration of the appearance or manifestation of Christ to the world at his baptism. Thus, January 6th was observed to be both Jesus’ baptism and birthday. “Epiphany… on the 6th of January… is mentioned by Clement of Alexandria (c. 155-220).” Later when the birth was changed to Dec. 25th, a special feast was added to Jan. 6th in celebration of the coming of the Three Kings (Magi) and a concurrent observance of gentile missions. (Schaff, History of the Christian Church)
Early mention of Jesus’ birth by Clement of Alexandria on May 20th. “The first evidence of the feast is from Egypt. About A.D. 200, Clement of Alexandria (Stromata I. 21) says that certain Egyptian theologians “over curiously” assign, not the year alone, but the day of Christ’s birth, placing it on 25 Pachon (20 May) in the twenty-eighth year of Augustus.” (newadvent.org)
Earliest mention of December 25 is in the Philocalian calendar representing Roman practice of the year AD 336, which states “natus Christus in Betleem Judeae.” “…during the consulship of (Augustus) Cæsar and Paulus Our Lord Jesus Christ was born on the eighth before the calends of January (25 December), a Friday, the fourteenth day of the moon.” Cyril of Jerusalem wrote to Pope Julius I (337-352) and asked for an authoritative judgment based upon census documents brought from Jerusalem to Rome by Titus after the destruction of the Temple in AD 70. Julius assigned Dec. 25th according to this correspondence, which may not be legitimate “At Rome, then, the Nativity was celebrated on 25 December before 354; in the East, at Constantinople, not before 379.” (newadvent.org )
Gregory Nazanzian (known for his defense of the two natures but single personhood of Christ) sought to initiate December 25th c. 379 or 380. This date could have been chosen to challenge the celebration of Natalis Solis Invicti or The Invincible Sun, (Oxford Dictionary of Christian Church) which was associated also with Mithra. That celebration was established by Emperor Domitian (reign AD 81-96) in the 90’s and affirmed by Trajan (reign AD 98-117). It reached the climax of popularity under Aurelian in 274 (newadvent.org).
It would seem that the church chose to celebrate the birth of Christ, who was prophesied to be “the Sun of Righteousness with Healing in His wings” (Malachi 4:2) to prove to the world that Jesus is the Son of God who conquered death and is the true invincible Son. “But Our Lord, too, is born in the month of December . . . the eight before the calends of January [25 December] . . ., But they call it the ‘Birthday of the Unconquered’. Who indeed is so unconquered as Our Lord . . .? -Cyprian (4th century)
Additionally, there we other winter celebrations in Rome around this time: Saturnalia, Sigillaria, Junenalia, Brumalia. The traditions connected to these festivals continue to influence our celebration of Christmas today: giving of presents to children, Christmas trees, lighting of candles, and the many excesses we attribute to contemporary culture of consumerism are actually ancient and never detached from Christmas. “while it also betrays the origin of the many excesses in which the unbelieving world indulges at this season, in wanton perversion of the true Christmas mirth” (Schaff). This, in spite of the fact the the church sought to create a somber season of reflection and repentance during Advent. There is an early tradition that dates the birth of Christ from his Annunciation by the Angel Gabriel, which was celebrated on March 25. There is a tradition also, that Jesus was conceived and crucified on the same day (March 25).
Dec. 25th Western Rite.
“The day is celebrated in the Western Rite by three Masses, of the night (normally said at midnight), of the dawn, and of the day, which have been held to symbolize the threefold birth of Christ, eternally in the bosom of the Father, from the womb of the Virgin Mary, and mystically in the soul of the faithful.” (Ox Dict. Chr Chur)