Christmas:

"Some Christians say that since the world celebrates Christmas—although it is becoming more and more politically correct to refer to it as ‘the holidays’—Christians should avoid it. But that is the same argument made by false religions that deny Christ altogether, as well as cults such as the Jehovah’s Witnesses who deny His deity. Those Christians who do celebrate Christmas often see the occasion as an opportunity to proclaim Him as ‘the reason for the season’ among the nations and to those trapped in false religions...

...[T]here is no legitimate scriptural reason not to celebrate Christmas. At the same time, there is no biblical mandate to celebrate either."  Full text:  Should Christians celebrate Christmas  http://www.gotquestions.org/Christian-Christmas.html

Christmas Trees:

"The modern custom of a Christmas tree does not come from any form of paganism. There is no evidence of any pagan religion decorating a special holiday tree for their mid-winter festivals, although the Romans celebrated the winter solstice with a festival called Saturnalia in honor of Saturnus, the god of agriculture. They decorated their houses with greens and lights and exchanged gifts. Late in the Middle Ages, Germans and Scandinavians placed evergreen trees inside their homes or just outside their doors to show their hope in the forthcoming spring. The first Christmas tree was decorated by Protestant Christians in 16th-century Germany. Our modern Christmas tree evolved from these early German traditions, and the custom most likely came to the United States with Hessian troops during the American Revolution, or with German immigrants to Pennsylvania and Ohio."  Full text:  Should we have a Christmas Tree? Does the Christmas Tree have its origin in ancient pagan rituals?  http://www.gotquestions.org/Christmas-tree.html

Birthdays:

"There is no specific prohibition against celebrating birthdays in Scripture, nor is there anything to indicate we should celebrate them. Scripturally speaking, it is a non-issue. The Bible does mention two individuals celebrating birthdays; the Egyptian Pharaoh in Joseph’s time (Genesis 40:20), and King Herod in the time of Jesus (Matthew 14:6; Mark 6:21). Some point to these non-believing individuals as evidence that celebrating birthdays is wrong, some form of pagan ritual. However, the Bible does not state, or even hint, that it was wrong for Pharaoh or Herod to celebrate their birthdays. Neither does Scripture anywhere discourage anyone from celebrating a birthday..."  Full text:  Should Christians celebrate birthdays?  http://www.gotquestions.org/Christian-birthdays.html

Holidays:

"...[T]he Bible does not speak against celebrating holidays. The Bible mentions several “celebrations” that the Israelites observed: Passover, Pentecost, Purim, New Moon, etc. The difference between these holidays and the holidays celebrated today is that some of our modern holidays have pagan or even anti-Christian origins. Christmas and Easter began as attempts to redefine a pagan holiday with a Christian meaning, i.e., the Easter bunny, the Christmas tree, giving gifts, hunting for eggs, etc.

That leaves us with a difficult decision – should we continue a practice that was started as a pagan religious ritual? Here are a few things to consider: (A) Does the holiday in any way promote false doctrine or immorality (Galatians 5:19-23)? (B) Can we thank God for what we observe on a holiday (1 Thessalonians 5:16-18)? (C) Will celebrating the holiday detract from your Christian testimony / witness (Philippians 2:15)? This is a decision a Christian family needs to make together. Pray to God, asking Him what He would have you to do (James 1:5)."  Full text:  Should a Christian celebrate holidays? http://www.gotquestions.org/Christian-holidays.html