Most Christians celebrate Christmas as a special holiday of giving to others with perhaps only slight recognition of the fact it is the supposed birthday of Jesus. Probably, that birthday was later during the year ( because it was reported there were shepherds in the fields with their flocks at about that time ). The actual birthday doesn't matter, because neither Jesus or his disciples ever suggested remembering his birthday. Jesus seemed to be a person who preached the spirit of laws rather than rote celebration, with the possible exception of the last supper; it is assumed by many Christians that the command to his disciples to participate in that ceremony extended to all later followers. I don't think there will be any divine grading points one way or the other regards observance of a holiday such as Christmas.
Before someone accuses me of being a scrooge on the point, I am a Christian and do like Christmas and have no problems with participation therein.
When I was a child my church did not even have a service on Christmas Day they do know but not then. Christmas day was as you say a day for giving and receiving presents.