The word Christmas has been around for centuries. Some dictionaries say it belongs to the late Old English period; others that it dates back to the 12th century. Old forms include cristes masse and christmasse, meaning the festival (mass) of Christ. Christmas actually replaced a number of significant pagan midwinter festivals when the church was trying to persuade Romans to convert to Christianity.
In the phrase Merry Christmas, the word merry does not refer an excess of seasonal good cheer, nor yet to drunkenness. Those meanings date from the 14th century onwards. However, the original meaning of merry was pleasing or agreeable. That meaning is also found in the phrase God rest you merry, gentlemen (NOT God rest you, merry gentlemen), where rest is used in the same sense as in rest assured.
The use of the abbreviation Xmas drives some people crazy, yet it is not a modern aberration, but an ancient usage. X was used to represent the Greek symbol chi, which is also the first letter in Christ. That usage has been around since Roman times.
Bringer of gifts Santa Claus has evolved from a Christian saint, Saint Nicholas, and is believed to have arrived in the US with the Dutch. Though now the two are inextricably intertwined, Father Christmas predates Santa Claus, having been around since the 15th century.