Was Christmas a replacement of the Jewish festival of Hanukkah that was celebrated by the early Christians or was it to replace the Pagan festival of the 'Invincible Sun' instituted in 274 CE.
Christmas has no biblical origins, it is meant to celebrate Jesus's birthday. In fact the church recognized Christmas's pagan origins and banned in England in 1647. Reformation in the 19th Century
In America it was banned between the years of 1659-1681. Christmas as we know it really didn't start happening until the late 1800's and even then it was foreign to most people. Puritans then where preaching and distributing literature denouncing such celebration. Christmas really became what we think of it today, when in 1843 Charles Dickens wrote "A Christmas Carol".
History aside, now we look at the origin of Christmas itself.
Dies Natalis of Sol Invictus, or that is the birthday of the unconquerable sun. It is also called Saturnalia as it Honors the deity Saturn. Saturn was worshiped for agricultural purposes. This was later celebrated by the Romans as Dies Natalis of Sol Invictus. It celebrated the renewal of light and the coming of the new year. What day was it celebrated on? You guessed it December 17-23 and 25. Saturnalia was celebrated with feasting, partying, and gifts. Saturnalia
As the Roman empire came under Christian rule pagan holidays where added to help convert pagans to Christianity. You see this mainly under emperor Constantine's rule. The people whom the Romans conquered had their "religion" and celebrations added to the Romans celebrations. The Romans may have gotten this from Persia. who had done this before in history.
Emperor Constantine did not really become a christian until later in life and even then he didn't stick with just Christianity. One or the other wasn't an option for him I guess. Constantine supported both Christianity and pagan beliefs. Constantine.
The names of Saturnalia where later changed to take on a more Christian aspect. The church commemorated December 25 as Jesus's birthday. The church got pagan converts and the pagans got to keep their holidays. Christmas origin
We know that Jesus could not have been born in December or January. The bible tells us that at Luke 2:8
So when Jesus was born we see that people where out sleeping in the field and watching sheep most of the day. Lets see what the bible says about that months weather conditions. Ezra 10:13
It was not even possible to stand outside it was so bitter cold. That is rain aside. Shepherds would not have been outside after late October let alone December.
Changing the name of the holiday doesn't change the pagan roots. Christmas doesn't celebrate Jesus's birthday, but a celebration by pagan devotees of Mithra. Mithra the Pagan Christ
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Why should Christmas be meant to replace anything?
The liturgical year is riddled with merriment, every other day is a feast or a solemnity or at least an observance of some pious memorial.
Other than to denounce Christ or the Churches that keep Christmas, there is no reason to conflate some pagan festivity no one cares about with Christmas. If there was a conspiracy back in the fourth Century, then St. Augustine would have said something about it. What he did say was that when the barbarians came to sack Rome, they left the churches alone, out of respect for traditions that were foreign to them, but which they could see were clearly holy. They didn't see in them their own idolatry, they saw the city of God made manifest.
Hanukkah on the other hand, has never been as big a thing as Christmas. Christmas has been an important marker in the eyes of the Catholic Church purely out of necessity. Consider the lectionary and how the Bible itself was formed. The books we use at Mass were the same books and letters mentioned by St. Justin Martyr when he wrote about what it is that Christians do during their get togethers. Naturally, a book can't go on ad infinitum so it makes sense that at some point you're going to finish the book and start over again. So, it makes sense that you'd want to put the events leading up to Jesus' birth in the first part of the book and go on from there.
So, we know Jesus died around Passover, we posit that the two most important truths in history took place on the same day of the year (The Incarnation and The Resurrection) and we do a +=9 months to get a good approximation of where Christmas should be.
Pagans and Jews aside, the question to be asked is, is there really a better day for Christmas?
The Hanukkah festivals that Jesus took part in was similar enough to Christmas in ritual and custom to assume that early Christians continued with the festival in honor of the birth of Jesus - that might well have fallen on the same day of the year.
Back then, the Feast of the Lights (Hanukkah or 'Festival of Dedication') took place for two days on the twenty-fifth and twenty-sixth days of Kislev starting with the lighting of candles on the evening of the twenty-fourth. (The Judaic month of Kislev is almost the same as December.) Candles were then lit for a further six or possibly eight days. The specific reason for the festival of Hanukkah is to celebrate the victory of the Maccabees over the Seleucids and the result of that victory, which was the re-dedication of the altar in the Temple after three years when no services took place. In general, it celebrates religious freedom, the light that was lit in Israel for all people, and the spread of that light throughout the world.
The date was of particular importance in the Greek /Roman calendar and in the calendars of many of the ancient societies. On or roundabout this day the star Sirius (the brightest of all stars) that flies behind the earth in its path around the Milky Way is right overhead at midnight. When Sirius is overhead at midnight it means that the sun is at its furthest south and that summer is coming again. For this reason, the date had been associated in many ancient and not so ancient religions with the birth of a god or a new period of religion. It was therefore no accident that Antiochus Epiphanes offered the first sacrifice to Zeus Olympios in the Temple on this date in 167 BCE. It was intended to show that a new period of rule of the Greek gods over the land had begun. Judah Maccabeus would have been fully aware of this and made sure that the first Hanukkah also fell on 25 December 164 (165) BCE to counter the Greek claim. (Now upon the same day that the strangers profaned the Temple, on the very same day it was cleansed again, even the five and twentieth day of the same month, which is Kislev - II Maccabees 10: 5)
Persia was different from the other countries in their beliefs around Sirius, and used the star to make predictions. This is based either on changes in color (white, blue, emerald) the star undergoes (in the past there were times when it has appeared red) or on the positional shift in relation to the background stars due to the gravitational influence of a white dwarf companion star. Because these changes are minute and dependent on great knowledge, it is no surprise that nobody but the magoi noticed them. (This would explain why Herod and the scribes did not notice it. If a huge big comet hung over Bethlehem, millions of people would have turned up, as they were strong believers in the magic of stars.)
Because it is closely linked with the Feast of the Tabernacles (Succoth), so close that it is even called that, and now see that that ye keep the Feast of Tabernacles in the month Kislev - II Maccabees 1: 9, it is a festival for all people (including gentiles) to celebrate. To the original promise made in the desert by the festival of Sukkoth (that one day Israel would no longer live in tents but in houses) the important facet of lights were added. With the rededication of the Temple, came the profound moment of the lighting of the candelabra. They made also new holy vessels, and into the temple they brought the candlestick . . . and the lamps that were upon the candlestick they lighted, that they might give light in the temple - I Maccabees 4: 49 - 50. Josephus said (Antiquities of the Jews, 12: 7: 7), and from that time to this we celebrate this festival, and called it Lights. I suppose the reason was, because this liberty beyond our hopes appeared to us; and that thence was the name given to that festival.
The festival is supposed to be a happy time in accordance with I Maccabees 4: 59 - the days of the dedication of the altar should be kept in their season from year to year by the space of eight days, from the five and twentieth day of the month Casleu, with mirth and gladness. From the earliest, the festivalgoers bare branches, and fair boughs, and palms also, and sang Psalms - II Maccabees 10: 7. Israel in winter is green as this is the time of the rains and what snow there is (if at all) quickly melts. Bringing greenery into the home therefore has nothing to do with the pagan midwinter festival but with the promise made in the desert and celebrated during the Feast of the Tabernacles.
The twenty-fifth of December (Kislev) that became important to Christianity together with joyous songs and the Christmas tree and lights all originated in Hanukkah.