According to a Christian Research Institute article by David W. T. Brattston, almost all early Christian writers never mentioned anything about birthdays. Origen did but he was in the minority. He wrote that since pagan kings celebrated their birthdays, we shouldn't imitate them.
One example of celebrating birthdays is in Genesis 40:20 (KJV). "And it came to pass the third day, which was Pharaoh's birthday, that he made a feast unto all his servants: and he lifted up the head of the chief butler and of the chief baker among his servants."
Another example is Matthew 14:6 (KJV). "But when Herod's birthday was kept, the daughter of Herodias danced before them, and pleased Herod." During the party, John the Baptist was beheaded.
But we need not lose our heads over the celebrating of birthdays. In fact, it's a show of love toward the celebrant.
As for Christmas, the secular part does have pagan roots. Nevertheless, we don't commit idolatry if we decorate our homes. As Paul wrote in 1 Corinthians 8:4 (KJV) about food offered to idols, "As concerning therefore the eating of those things that are offered in sacrifice unto idols, we know that an idol is nothing in the world, and that there is none other God but one."
Neither should we condemn others for minor things such as celebrating holidays. Paul said in Romans 14:5 (KJV), "One man esteemeth one day above another: another esteemeth every day alike. Let every man be fully persuaded in his own mind."
My only objection to Santa, as well as the Easter Bunny and the Tooth Fairy, is that parents convince their children that those characters are real. It's better to pretend that they're part of a make believe game. That way, children aren't devastated when they learn they've been lied to.
I'll be writing more about this prohibition and other errant doctrines in my next book called You Think You're going to Heaven? Many people have turned from believing in God because they place him in with Santa and other childhood story characters. They totally miss the boat, so to speak, because of foolish parents lying to them.