Christmastime is the stretch of days around Christmas, not only the 25th. People mean late December, and often a little of early January, when lights are still up, school is closed, and families visit. It names a season the way summertime names summer. You will hear it in songs, cards, and stories more than in quick daily talk; many people just say at Christmas or over Christmas. That is not because Christmastime is wrong — it is a fuller, slightly story-like way to name those days. Some writers split it as Christmas time, two words; it is the same idea.