In addition to what Jon `C said, the practice of yearly celebrating a person's birth did not yet exist. IIRC, the Roman Empire was putting pressure on Christians (or something like that), and the church adopted holidays during the time of Pagan celebrations. If you look closely at them, you will see the similarities. Easter, to Pagans, is a celebration of life and fertility. To Christians, it is a celebration of the resurrection of Christ. Christmas (or at least some time during this season) was a celebration of the birth of a Pagan god (whose specific name I can't remember). So Christians adopted the celebration of the birth of Christ. Originally, Christmas was not December 25, but is documented as being celebrated on various dates, both earlier and later than Dec. 25, and even as late as sometime in January.
Actually, the earliest documented use of a Christmas tree wasn't until 1521 in the German region of Alsace. There isn't evidence to support that the Christmas tree derived from the Yule Tree either. Rather, the evidence shows that it decended from the Paradise Tree and the Christmas light of the Middle Ages.