Strictly forbidden in the Bible? I don't think so. I din't see the videos in the article you posted, I have heard enough of people saying Christmas is pagan and that it is wrong. Can you tell me where exactly it says in the Bible that it is wrong? I have researched on this before and I like to share that with you.
The way we celebrate Christmas depends on our attitude towards Christmas, our reason to celebrate Christmas, our spirit towards it. You can do it in a negative way, or a positive way. Titus 1:15 tells us this "To the pure all things are pure, but to those who are defiled and unbelieving nothing is pure; but even their mind and conscience are defiled." I'll tackle this subject point by point.
1) The first issue is about the date, no one can be sure about when Christ was born. How December 25th came up? Chrysostom (A..D. 345-407) in 386 stated that December 25th is the correct date and hence it became the official date for Christ's birth except in the Eastern church which still retained January 6th. Here you can see that some of them considered Christ's birth to be in January and some in December. Why these two months? Here's why -
An archeologist who lived in Palestine for years studying this, James Kelso, had this to say -
"The best season for the shepherds of Bethlehem is the winter when heavy rains bring up a luscious crop of new grass. After the rains the once-barren, brown desert earth is suddenly a field of brilliant green. One year when excavating at New Testament Jericho, I lived in Jerusalem and drove through this area twice every day. At one single point along the road, I could see at times as many as five shepherds with their flocks on one hillside. One shepherd stayed with his flock at the same point for three weeks, so lush was the grass. But as soon as the rains stopped in the spring, the land quickly took on its normal desert look once again."
Since there seem to have been a number of shepherds who came to see the Christ child, December or January would be the most likely months (James Kelso, An Archaeologist Looks At The Gospels, p. 23-24).
Since we don't know the exact date, we choose the best probable one we know.
2) About Santa being anagram of Satan. Here's how Santa came into the whole picture of Christmas - The Santa Claus idea originated with a man by the name of St. Nicholas who was the Bishop of Myra in Lycia in the area of present day Turkey. He went about, often at night, giving gifts to poor and needy children. He later became the patron saint of children in the Roman Catholic Church. From here the story grew and became legend in country after country with various details were deleted and added as the legend of St. Nick grew.
Nowadays, people and kids confuse Santa to be Jesus which is wrong. Certain kids don't even know what Christmas is about other than receiving gifts. Parents must teach their kids that Christmas is about Jesus and his birth and also a time to give.
3) Scriptures doesn't say celebrating Christmas is wrong in the New Testament. But celebrating a festival of the Old testament is wrong because it was before Christ. We can see that in Colossians 2 passage. The New testament is silent about Christmas, if you say that is valid enough, then there are many things the New Testament is silent about. For example, The Holy Communion was done everyday during ancient times, we only do it once a week. Why? Because it isn't a binding rule, no where is it said in the Scriptures that we must have the Lord's Supper everyday. They did it everyday due to their love and spirit for Christ. Similar for Christmas.
4) Christmas had adopted many things during the years from different countries. The tree is a result of this and some say this is paganism. The everygreen tree can resemble something else -
"The evergreen tree is a symbol of the eternal life which Christ, the Son of God, offers to man via another tree, the cross (Rev. 2:7; 22:2, 14).
The presents under the tree can remind us of God's gift and our need to give of ourselves to others as those who have received God's gift of life through Christ."
That is quoted from the article I learned all this from. End of the day it all comes down to how we celebrate it. Making Christmas as a festival for gathering together and drinking is very wrong. That's how it is done in majority of the places these days. If you celebrate Christmas in a positive manner, it isn't wrong. Plus you can celebrate Christmas everyday by giving to others and giving your praise and thanks to God for sending us His Son.
Sorry for the long post x_x. God Bless you!