He wasn't. Where Jesus was born is similar in climate to the US. Meaning, there's no way shepherds would have their sheep outside during the night in the middle of the winter.
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How do you know the place Jesus was born has the same climate as the US, let alone US after 2000 years? Not to mention a specific place of Jesus' birth isn't even historically established. Also, what do the sheepes have to do with anything?
Now about the articles you've linked...
The first one just lists statements without linking any sources. They don't specify wich holidays the Christians supposedly stole, they assume too many things without saying why exactly, and they raise the points wich I refuted in my longer post above. Not only that, but the people they quote assume that the Church invented Christmas to stop people from finding out that Jesus never existed, a Christ myth theory that has been proven wrong. (It's debatable wether such ideas were even present at the time.)
The second link leads to a Jewish blog. Now, when you do research on these things you don't rely on the sides who are in one way or another affiliated with the subject. You first look at the neutral/objective parties and see what they have to say, and only then go into individual sides to see their sides of the story. A jewish blog like this (wich doesn't go by the said criterium but I'll get to that) is biased. Now I'll tackle the core of the blog.
The central idea of the blog is that Christmas is a hijacked version of a Roman festival Saturnalia. First, they claim that the festival of Saturnia lasted on December 25th, wich is a lie. The festival was celebrated on December 17th, and only later, when the Julian Calendar was put in place, was it expanded to last until December 23. Nowhere does it say the festival lasted to 25th, as a matter of fact, Saturnalia served as a tie-in to the Winter Solstace, wich I've already dealt with in the post above, and even it doesn't fall on 25th but rather on 24th, so the author of the blog clearly flasified his information to make it seem like the exact date of Christmas.
Then, a historian by the name of Lucian is mentioned. The author claims that Lucian wrote about the terrible pracitces of Saturnalia, and asserts that these practices have been kept by the Christians in the early phases of what would later become Christmas. Now the lack of sources comes to light. The author, througt the blog, only gives sources to selected parts, but shows nothing when delivering the big statements like the one just said.
Afterwards, the author quotes a few other works, and adds his own assumptions to the basis of what has been sourced. This is the case when the blog gets to Puritans, who, contrary to the author, didn't ban Christmas due to it's "known pagan origin", but rather due to pagan customs. Various crimes commited by the Catholic Church officials are also mentioned but with a fabricated background of it all spamming from Saturnalia.
The blog mentions authors and their works, wich I can find virtually no reviews of, no articles what so ever (if you have info please share), is written in a highly militistic tone, especially visible in the last part where he calls out Christians as being a "curse to Torah".
In short, it's a biased blog, with much of it's info being unconfirmed, only partially true or downright false.