Should Christians celebrate a Holiday based on a pagan festival commemorating a false god?

Video - Should Christians Celebrate Christmas? Is Christmas a Pagan Holiday? - Hank Hanegraaff

Christians didn’t choose this date to Christianize a pagan festival and worship the sun. This date was intentionally chosen as a rival celebration to celebrate the Son of God who became flesh. A Christmas tree surrounded by gifts is fitting and can be a reminder of the Savior who gave the greatest gift of all, eternal life for those who place their trust in Him. [ 1 ] 

Isaiah 7:14

Therefore the Lord Himself will give you a sign: Behold, the virgin will conceive and give birth to a son, and she will name Him Immanuel.

The prophecy  in Genesis (Gen 3:15) was given to Satan. Was King Herod influenced by Satan to slaughter children in an attempt to kill Jesus? God's sovereign plan can't be undone. God isn't behind the scenes hoping people will make this or that choice to fulfill His plan. Jesus was nailed to a cross by the hands of godless men by the predetermined plan and foreknowledge of God. Jesus didn't defeat Satan by stepping on the head of a figurative snake, although this is the imagery used. He defeated Satan on the cross, disarming the rulers and authorities. He made a public display of them, having triumphed over them (Col 2:15). Satan didn't want Jesus to go to the cross. So when Peter echoed this idea, Jesus responded "Get behind me Satan" (Matt 16:23). 

Genesis 3:15

And I will make enemies of you and the woman, And of your offspring and her Descendant;

He shall bruise you on the head, And you shall bruise Him on the heel.”

Jeremiah 31:15

“A voice is heard in Ramah, mourning and great weeping, Rachel weeping for her children and refusing to be comforted, because they are no more.”

This personification, that is, an imaginary person introduced: for the Prophet raises up Rachel from the grave, and represents her as lamenting. She had been long dead, and her body had been reduced to ashes; but the discourse has more force when lamentation is ascribed to a dead woman than if the Prophet had said, that the land would present a sad and a mournful appearance, because it would be waste and desolate; for rhetoricians mention personification among the highest excellencies, and Cicero, when treating of the highest ornament of an oration, says, that nothing touches an audience so much as when the dead are raised up from below. The Prophet, then, though not taught in the school of rhetoricians, thus adorned his discourse through the impulse of God’s Spirit, that he might more effectually penetrate into the hearts of the people.This passage is quoted by Matthew, (Matt 2:18) where he gives an account of the infants under two years old, who had been slain by the command of Herod: then he says, that this prophecy was fulfilled, even that Rachel again wept for her children. But the explanation of this is attended with no difficulty; for Matthew meant no other thing than that the same thing happened at the coming of Christ as had taken place before, when the whole country was reduced to desolation; for it was the Evangelist’s object to remove an offense arising from novelty, as we know that men’s minds feel a dread when anything new, unexpected, and never heard of before happens. Hence, the Evangelists often direct their attention to this point, so that what happened in the time of Christ might not terrify or disturb the minds of men as a thing new and unexpected, inasmuch as the fathers formerly had experienced the same. To no purpose then do interpreters torture themselves by explaining this passage allegorically; for Matthew did not intend to lessen the authority of ancient history, for he knew in what sense this had been formerly said; but his only object was to remind the Jews that there was no cause for them to be greatly astonished at that slaughter, for that region had formerly been laid waste and bereaved of all its inhabitants, as though a mother, having had a large family, were to lose all her children [ 2 ].  Rachel was buried in Bethleham (Gen 35:19). The prophecy is about a massacre of children would happen at Messiah's birthplace.

Micah 5:2

But as for you, Bethlehem Ephrathah, Too little to be among the clans of Judah, From you One will come forth for Me to be ruler in Israel.

His times of coming forth are from long ago, From the days of eternity.”

Matthew 2:1-6

Now after Jesus was born in Bethlehem of Judea in the days of Herod the king, behold, magi from the east arrived in Jerusalem, saying,  “Where is He who has been born King of the Jews? For we saw His star in the east and have come to worship Him.” When Herod the king heard this, he was troubled, and all Jerusalem with him. And gathering together all the chief priests and scribes of the people, he inquired of them where the Messiah was to be born. They said to him, “In Bethlehem of Judea; for this is what has been written by the prophet: ‘And you, Bethlehem, land of Judah, Are by no means least among the leaders of Judah; For from you will come forth a Ruler Who will shepherd My people Israel.’”

Matthew 2:16-18

Then when Herod saw that he had been tricked by the magi, he became very enraged, and sent men and killed all the boys who were in Bethlehem and all its vicinity who were two years old or under, according to the time which he had determined from the magi. Then what had been spoken through Jeremiah the prophet was fulfilled: “A voice was heard in Ramah, Weeping and great mourning, Rachel weeping for her children; And she refused to be comforted, Because they were no more.”

Video - How ‘the war on Christmas’ became a political rallying cry - PBS

Does Jeremiah 10 forbid Christmas trees?

No. This is a reference to wooden idols, not Christmas trees. Christmas trees originated in Germany 2000 years after Jeremiah’s condemnation of wooden idols. In the 16th century, Christmas trees evolved overtime from two traditions: 

1) The Paradise Tree: This was hung with apples as a reminder of the tree of life in the Garden of Eden.

2) The Triangular Shelf: A shelf holding figurines decorated by a star. [ 1 ] 

Jeremiah 10:2-4

Thus says the Lord,“Do not learn the way of the nations, And do not be terrified by the signs of the heavens although the nations are terrified by them;

For the customs of the peoples are delusion; Because it is wood cut from the forest, The work of the hands of a craftsman with a cutting tool.

“They decorate it with silver and with gold; They fasten it with nails and with hammers so that it will not totter.

Saint Nicholas

Saint Nicholas was a real person who provided gifts for needy children. He supported the doctrine of the Trinity at the Council of Nicea in 325 A.D. He was a hero of the faith. 

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Cited Sources: The Bible Answer Book by Hank Hanegraaff  [1 ] , John Calvin Commentary [2 ],