Is Christmas Really Pagan?

Some claim that Christmas originated after a pagan festival. They equate the season with a pagan theme after the winter solstice, also to do with Mithras, Saturnalia, and other Roman worship dieties. They state that it is the Sol Invictus worship of the Unconquored Sun. However, others defend its origins to say that Christians originally celebrated the birth of Christ and pagans mimicked it after Christians. Which is it? 

We look at the traditions as well as search for the origin of the December 25 date that many recognize as the commemoration of the birth of Jesus Christ.