"Santa" is based off of St. Nicholas. This site explains the legend/history of St. Nicholas:

http://www.umkc.edu/imc/stnick.htm

In summary, it states:

"The story of St. Nicholas, also called Nicholas of Bari and Nicholas of Myra (and Santa Claus), began in what is now Turkey, early in the fourth century, near the modern Turkish city of Finike. One of the most popular minor saints commemorated in the Eastern and Western churches, his feast day is December 6th. He is now traditionally associated with the festival of Christmas."

I believe the tree and St. Nich and gift giving parts of Christmas used to be separate from the religious observation of Christ's birth long long ago, but when Christmas came to be combined with other celebrations over time until it became a combination of different things for different people. As mentioned about Yule Tide, some of those things were incorporated into "Christmas." I think if you did a search on the net and put in things like "History of Christmas trees" or "History of Santa" etc, you'd come up with a lot of reading too.