The question you pose is a huge ongoing debate among Christians.
While many of the arguments in favor of doing away with any holiday connected to pagan traditions are based upon truth, in so far as they go, they ignore a logical point.
All pagan traditions are a bastardization of an element of God's truth or creation. For example, the Christmas tree: before the pagans took the tree into the house, it was God's creation and He pronounced it " GOOD" (Genesis 1:12). The same goes with rainbows, and dolphins and eggs and stars and bunnies. Many of God's GOOD things are misused by evil. That does not change the fact that He created them and called them GOOD.
Worshipping the tree would be quite a different story, forbidden by God; but is that what Christians who celebrate Christmas are doing, or are they celebrating the birth of Jesus, whom alone they worship? Further, is that what Christians appear to be doing in the eyes of the world (worshipping the tree), as that would not be a good witness? No, the world does not see Christmas as a day when Christians worship a tree.
The following verse, from the New Testament, is most appropriate to this question. While thinking about this issue, one needs to follow the argument of those against the celebration of any holiday related to paganism to it’s logical conclusion.
We now have, in the celebration of Christmas, a day when the whole world stops and acknowledges (whether at a personal level or not) the birth of the Savior of the world, and the soon coming King. When songs are sung about His glory, and cards are sent reaffirming the message the Jesus IS HERE ! When love is strewn about liberally, giving the world a foretaste of Heaven!
Do we really want to toss this tradition, with it’s incredible opportunity, into the wastebasket of history ? Do we want to, in essence, throw the baby out with the bath-water? How happy Satan would be !
Not me! Next Christmas, when you hear a prancing and pawing on the roof, it won’t be Santa and his sleigh-- it will be me, shouting the news from the rooftops: "Unto YOU a SAVIOR is BORN !"
Col 2:13 And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses;Col 2:14 Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross;
Col 2:15 [And] having spoiled principalities and powers, he made a shew of them openly, triumphing over them in it.
Col 2:16 Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath [days]:
Col 2:17 Which are a shadow of things to come; but the body [is] of Christ.
Having stated the above, a caveat needs to be added: Halloween, (contrary to the traditional meanings of Christmas and Easter), is an outright pagan holiday, having nothing whatsoever to do with Jesus Christ. It is rather, a celebration of Satan, and as such should be an anathema to all Christian believers everywhere !