Remember that the celebration of Christmas was not one of the original feasts related to the mystery of Christ celebrated by the ancient Church. Among all the feasts of the Church the most important was the Celebration of Resurrection of Christ or Passover, or Pascha, because it was His resurrection that sealed His Messianic role and perfect divinity. The second most important feast was the Baptism of Christ during which the Father revealed to the world that Jesus was His beloved Son through the descent of the Holy Spirit in the form of a dove and this feast is generally called Epiphany, but easterners love to call it Theophany, because it was the manifestation of Christ as God. In the East these were the most important feasts concerning the mystery of Christ.
Things changed in the Church after Constantine the Great declared freedom for the Church in the beginning of the fourth century. The feast of Saturnalia, a licentious celebration of the winter solstice dedicated to Saturn, was Christianized by the Church of Rome to attract the Roman pagans to Christianity. Saturnalia had many features: As the nights became longer and darker with the arrival of winter the display of light everywhere became an important observance of the feast. With winter comes the cessation of life, particularly the vegetation; and in order to give hope of life to a frozen world of winter the display of evergreen plants and green wreaths in general was also another feature. Such practices easily found their ways into the Christianized feast, now called the feast of the Nativity of Christ (Christmas is an Anglo-Saxon rendering of the same feast), with the emphasis that Christ, who was the ultimate light and the light of light, became the new focus of the celebration; and the Roman Christianized pagans began to celebrate the birth of Christ, the light of light in conjunction with the Saturnalia celebrations.
From Rome, which was the center of the civilized world then, the celebration moved to the East, where it was not welcomed as it had been intended by the Romans. Although the Eastern Christians did not oppose the idea of a feast of the nativity of Christ, they did not embrace the date it was observed in Rome, for the simple reason that Saturnalia had no meaning for them. They accepted the feast and placed it immediately attached to Theophany. Hence, the feast of nativity of Christ was celebrated on January 7 every year, some even celebrated it with Theophany. It was at this time all Orthodox Christians and other eastern Christians celebrated the feast of Nativity. In recent times, we see that the Orthodox minorities in western countries have moved their observance of the feast of nativity of Christ along with their western brethren on December 25. However, we see that the majority of eastern Christians still follow January 6 or 7 as their Christmas day, for example, the Russians, Ukrainians and other eastern European Orthodox Christians, Armenians, Copts and Ethiopians. Please note that those Christians, who celebrate the nativity of Christ on December 25, also celebrate the annunciation to Mary on March 25 (exactly nine months prior to the birth of Christ).
Based on historical and circumstantial evidences the majority of scholars agree that Christ was not born in the winter; Christ’s birth took place some time in the autumn or spring according to them.
Then why don’t we change the date? We do not know the exact date. The most important idea is the observance of the truth of the nativity of Christ, for which a date does not matter much. Some