My humble thoughts:
Regarding Christmas and Easter having pagan roots, I'm reminded of Romans 14:5-8 -
5 One person esteems one day above another; another esteems every day alike. Let each be fully convinced in his own mind. 6 He who observes the day, observes it to the Lord; and he who does not observe the day, to the Lord he does not observe it. He who eats, eats to the Lord, for he gives God thanks; and he who does not eat, to the Lord he does not eat, and gives God thanks. 7 For none of us lives to himself, and no one dies to himself. 8 For if we live, we live to the Lord; and if we die, we die to the Lord. Therefore, whether we live or die, we are the Lord's.
In my mind, every day is set apart to celebrate Christ in thought, word and deed. However, as a family, we find no objection to our conscience to put up a Christmas tree, give presents and have people over for a special dinner on or around December 25th.
Unfortunately, there are some subtle compromises with the world that many Christians have adopted in respect to Christmas.
One such issue is Santa Claus. Yes, I know who Saint Nicholas was but our modern day version of Santa Claus is nothing like the original disciple of Christ. And we have Christian friends who've taught their small children that there is a Santa Claus in the modern, American version (i.e. lives at the North Pole, flies in sleigh, etc). I find that objectionable for 3 reasons:
(1) Lying to your children
(2) when they find out that the Santa Claus you've been telling them about is a myth, will they wonder if Jesus is a myth as well?
(3) Why even introduce a silly myth when you can tell the greatest story of the Word being born as a little baby in Bethlehem.
For these reasons, my children will never "believe" in Santa Claus but rather will be taught the story of the little baby in Bethlehem. We have a interactive nativity scene that we are going through with our 3 year old to teach him the story of Jesus' birth.
Another issue surrounding Christmas is the rampant materialism. Many people are caught up in what they will get. Even from giving perspective, we make it "noble" to give to others toys and items that they don't need. This is especially disturbing when we are surrounded by a world lost without Christ. If we want to reflect or represent the fact of God's gift to us, we should give to spread the Gospel. For this reason, my wife and I are working to limit the number of presents in our Christmas and to look for ways to teach our kids to give the Gospel (i.e. Samaritan's Purse - Operation Christmas Child). This is somewhat difficult as extended relatives want to lavish gifts upon our kids, but we're hoping to work to limit that. Another way to curb the materialism is implementing the "toy in, toy out" plan. This involves giving an existing toy away when a new toy is received.
Finally, I've become a little bothered this Christmas by condemnation of congregations who are having Sunday services on Dec 25 for the congregations who are not. I attend a church who is having both a Christmas Eve service and a sunday service on Christmas morning. The reason for the condemnation seems to revolve around the assumption that you must be in attendance at your local church in order to truly celebrate the birth of Jesus. While I'm not adverse to celebrating with my local part of the body of Christ, it doesn't seem charitable to condemn other Christians for celebrating the birth of Jesus with their families or choosing to celebrate His birth every other day of the year (see above Romans reference).
Anyway, those are my thoughts on Christmas.