Christians can't deny that some Christmas traditions are traced back to pagan celebrations and cultures. There are a couple examples:
**For the pagans winter celebration, ringing of bells were done to drive out the evil spirits. For the Christians, the ringing of bells were done to welcome in Christmas with joy and happiness. The Christians are reminded of the birth of Jesus.
**Pagans also used candle lighting to drive away the forces of cold and darkness. Christians light them at Christmas to rejoice in Jesus, the "Light of the World" - John 1:4-9.
**Druids offered gifts to their goats as part of a pagn ritual. In today's time, gifts are given to loved ones and friends. Biblically speaking, Jesus was the first and greatest gift ever given. The Magi, or Wisemen, gave gifts to Jesus, the child. His birth is considered worthy of celebration.
What's important to Christians is our traditions (of today) and what they mean to us as believers in Jesus. The origins of pagans had their traditions - however, the early believers, through the churches, wanted ways to celebrate Jesus's birth.
This is where personal choice comes in. If people don't want to celebrate a Christmas tradition because they believe it's too steeped in paganism, then they don't have to observe it. At the same time, if people feel that they can honor and worship God through a particular tradition, then they can observe it if they choose.
I would like to add, however, that there are also people who celebrate Christmas who aren't believers. They enjoy the tradition of family and friends getting together, dinners, presents, etc., without acknowledging anything Christian about it. There are other people who don't celebrate Christmas at all. That is their choice, as well.
Another thing I'd like to address is that it is said that it's documented that Jesus was born on December 25th. (There are some who disagree and since the Bible doesn't mention the exact date, apparently this is something we don't need to concern ourselves with.) The December 25th date coincided with the pagan festivals celebrating the winter solstice. The churches simply offered a Christian alternative for celebrating the birth of Christ and adjusted the ways of the pagans' celebrating to adapt to Christian ways.