The Bible gives us precedent to say Yes.
First, God’s people have always celebrated holidays that are not mandated in the Bible. To name two, the Feast of Purim was established in the 400s BC, when Esther and Mordecai saved the Jews from slaughter. The name Purim is the Hebrew form of a pagan, Babylonian word for “lots”. The feast began when “the Jews of the villages who dwelt in the unwalled towns celebrated the fourteenth day of the month of Adar with gladness and feasting, as a holiday, and for sending presents to one another.” Crucially for us, nowhere does God mandate it as a holy day, as he did Passover or Pentecost – it was a human decision.
Second, the Jews invented the holiday of Chanukah or Hanukkah, to celebrate every December how the Maccabees rededicated the Jerusalem temple in 165 BC, after it had been captured and defiled by the Syrian king. Also known as the Feast of Dedication, it was observed in Jesus’ day every winter, and Christ himself went to the temple in Jerusalem to attend it (John 10:22-23). Again, this was a holiday that the Jews invented to celebrate a remarkable chapter in their history; it is not “biblical.”
By analogy, Christians may create holidays to commemorate God’s actions in human history. The church has always had Holy Week and Pentecost, which mirror the ancient biblical feast days but which are now invested with deeper meaning. If Christians wish to celebrate Christ’s Second Coming during Advent, his birth on Christmas, and his resurrection on Resurrection Sunday, I say that’s fine – the events they commemorate are of exponentially greater consequence than those of Purim or Chanukah.
Christmas, and ‘tis the season to be jolly. Oh, and ‘tis also the season for people to claim that December 25 is a pagan holiday and should not be a celebration of Christ’s birth.
This is patently untrue, since some Christians believed that Jesus was born on December 25 as early as the year 200, and probably earlier. The calculation had nothing to do with the pagan Saturnalia feast, but rather was based on the idea that the earth was created on a March 25, that Jesus was conceived on that date and born exactly nine months later.
“But December 25 was a pagan holiday of gift-giving and decorating trees!” they tell me. Well, no it wasn’t, it was Dec 17-23. Anyway, if you take an ancient Roman calendar, and poke your finger at any date, and you will land on a pagan holiday that has some resemblance to Christmas. 
Celebrate Christ’s birth in May or July if you wish. If the date we honor is arbitrary, than changing it would be even more capricious, and odds are you’re going to land on July 4, Arbor Day, Lincoln’s Birthday or some other conflicting “wordly” date.
NOTES: Here is one example:http://www.lasttrumpetministries.org/tracts/tract3.html  Hippolytus, in his Commentary on Daniel 23.3, said “For the first advent of our Lord in the flesh, when he was born in Bethlehem, was December 25th [literally, “eight days before the kalends of January], Wednesday, while Augustus was in his forty-second year…”  http://www.novaroma.org/calendar/index.html
Visit Gary’s blog to comment on this article.
[author] [author_image timthumb=’on’]http://christmycovenant.com/wordpress/wp-content/uploads/2011/04/cmc-gary-shogren-sm.jpg[/author_image] [author_info]Copyright Gary Shogren.
Gary has a PhD in New Testament Exegesis. He serves as Professor at Seminario ESEPA, San Jose, Costa Rica[/author_info] [/author]