I was already aware of the speculation that Christs birthday was in the spring (how can they prove that), but Christians celebrate Christmas as a celebration of Christs birthday and how it affects mankind. Us christians dont buy a birthday cake and shit like that. The churchs I have gone to use the idea that a King was born, the son of God, and was the messenger of peace and hope for the world. It is less about the actual birth of Christ and more about how all of us today have a chance to repent, live in peace and harmony with our brothers. The church I used to go to used to say "Its Jesus birthday, not yours." And the preacher asked everyone to match how ever much they spent on presents and give it to a Sudan project. They built fresh-water reserves, set up schools and churches, and are setting up adoptions.
From what you are saying, it seems the day used to comemorate Christ's coming just happens to be the most brotherly and peaceful day, just by chance. It started out with people being nice to celebrate the new-born saviour. The holiday isnt meant to spread religion specifically, but the message of Jesus; that we should be kind to each other, help the less fortunate, protect our brothers, etc. Over the years, the religion has been downplayed, but the overall idea has stayed.