Even in Hindu religious tradition there is this Krishna Jayanti (birthday), and it's a national holiday for India. Hindus may argue that the point is not whether Krishna is an historical person or not; but that it's the belief of the people that matters. Similarly, the point is not whether Rama was born in Ayodhya or not; but it's the belief of the people that matters. In Hindu belief whether it's Krishna or Rama they are avatars (incarnate) of Vishnu. Vishnu would be born as an avatar whenever evil force must be punished, and thus he came as Krishna/Ram to put an end to the evil force.
Christians belief is different from that of Hinduism. For the Christians historical basis is extremely important. If Jesus was not an historical figure and his crucifixion and resurrection are all matters of just belief without historical basis Christians will cease to be worshipers of Jesus Christ. Christians appeal to history for their belief. Christians further believe that Jesus Christ came as man just once. So it's not really an avatar because in avatar incarnation happens again and again.
Thus, Christmas is the day when Christians celebrate to commemorate the day when God became man; to live with man as man. The Bible tells us through the songs of Zechariah and Mary that Jesus came to deliver the weak and the oppressed. God thus became man to bring justice and salvation for the humble, poor and the helpless. And that is the message of Christmas. To celebrate Christmas without having understood this dimension of deliverance is to miss out something important.
Let this Christmas bring a fresh understanding of who Jesus is and what it means to know him. And let God's spirit grant you strength to follow Jesus as your living guru, and in serving those who are in need-- spiritually, morally and physically.