Christmas is neither a biblical nor religious holiday (from the Lord's perspective). For many of those who belong to the Lord, they have adopted the same way of thinking as the Lord. There are, however, many who regard Christmas as a day, a special day to remember the Lord. Those who do that, that is up to them.
Consequently, in the Lord's church, there is no sanction from the Lord to recognize as a religious holiday anything about His birth; He came into the dark world in which we live because the Lord loved (and loves) us. Christians don't minimize His birth; they simply refuse to elevate it to such a high perch like so many others. Here is what Christians are to do: they are to recognize His birth, His life, His death, and His resurrection. This is done best in two areas: the life lived, and the worship engaged.
If there is a day to recognize, it is the first day of the week when the saints gather to meet with the Lord in worship. Thus, to the New Testament saint, the festive occasion that many celebrate and call "Christmas", to saints patterned after the teachings of the New Testament, the Lord's day is always a sacred day, a day wherein our privilege, opportunity, and responsibility is before us to worship Him who came into this world to seek and save the lost.
Whether you call the festivities associated with this time of the year (December) "Christmas" or "Holiday" or something else matters not (for it amounts to the same thing). What matters is one's heart and its willingness to submit to the Lord's teachings.