It would make sense that it would be η Χριστούγεννα if it were a literal translation of the English word Christmas, but it is not. One would also think that since the word Χριστούγεννα ends with an alpha (α) it would be a feminine noun and that's why it has the feminine article η. Christmas is usually a one-day affair in most countries, like the United States, and celebrated on December 25. In Greece, though, Christmas lasts longer than just one day. Many holidays or important occasions, like a Greek wedding, for example, can span over a four day period.
