Yes, Christmas is a Christian holiday. It literally means "Christ's Mass".
Part of the reason the Roman Empire fell apart was the Emperor Constantine's conversion to Christianity and the subsequent adoption of Christianity as the official religion.
In doing so, they began to adopt existing pagan festivals and customs and renamed them, and re-purposed them as Christian traditions, thereby making it easier for people of other religions to accept Christianity taking over. They basically kept doing the same thing and just called it something else.
In effect, the Roman Empire made Christianity into an unstoppable juggernaut at its own expense. Where the Empire would quickly fracture and crumble, Christianity would go on and on and on and on. There's irony for ya...
Thus, Saturnalia (the Roman festival honoring Saturn and the winter solstice) became Christmas, and it is from there that the traditions of gift-giving and merrymaking come. Christmas also absorbed traditions from a variety of other winter festivals such as the Roman New Year from which comes the tradition of greenery, lights, and charity, and from Germanic pagan feasts we get things like Yule Logs and various foods traditions.
Notably, the Norse god Odin became Santa Claus, and his eight-legged flying horse, Sleipnir, became Santa's eight flying reindeer. During the 12-day festival of Yule (which would become "Chirstmastide" AKA "The Twelve Days Of Christmas") Odin would lead a hunting party through the sky, and along his journey children would place their boots, filled with carrots, straw, or sugar, near the chimney for Sleipnir to eat. Odin would then reward those children for their kindness by replacing Sleipnir's food with gifts or candy. The tradition persists today as leaving cookies for Santa and hanging stockings by the chimney to be filled with candy and gifts.
That then became entangled with legends of Saint Nicholas of Myra/Sinterklaas(the Dutch name for him), which is where he got his name.....and finally the Coca-Cola Company got a hold of him and popularized the bright red suit that has now become the iconic image of the figure.
Christmas is the finest example of how Christianity pretty much ripped off anything and everything they could...