Augustus
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So given the current story of Santa Claus, Did St. Nicolas watch all children to see if they were good or bad as did Frau Holle. Did St. Nicolas then fly through the air delivering presents to good children and delivering coal and switches to those who were bad as did Frau Holle? Was St. Nicolas associated with snow/winter as Frau Holle?
St Nick was associated with his day on 6 Dec which was in the winter. The modern cultural representations are far too recent to be a cause of the celebration itself, the question is about to what extent the modern cultural representations are 'pagan'.
You get many things that might seem "pagan" as they are non-Biblical, but that ignores the large folk-Christian cultural contexts over 1500 years.
Something like Krampus looks 'obviously' pagan at first glance, but is more likely the product of medieval plays featuring St Nick and the devil. Ditto watching over children.
“A report from the late 1600s by the Augustinian monk Abraham a Sancta Clara of Vienna stresses this mostly academic function, describing Nicholas coming “to test the children and to examine whether they had been well instructed … in matters of faith, spelling, syllable divisions, reading, writing, arithmetic, and languages.”
Al Ridenour - The Krampus and the Old, Dark Christmas
The problem with these claims about Frau Holle though is that they are also likely to be far more modern than you think.
A load of "pagan" mythology is really roughly contemporary to the 19th c German Romantic tradition and volkische movement.
The works of Jacob Grimm set the tone for many of these ideas, but he tends to assume everything reflects an ancient context as he was motivated to construct a unifying German national identity based on an ancient lineage of Germanic myth. Simply assuming anything that looks 'pagan' is genuinely pagan despite the paucity of evidence is not particularly rigorous and modern scholars, with better evidence, often posit a much more recent origin for many of the folk tales.
Folk tales have always existed and evolved around common themes, but 'authentic' pagan traditions are unlikely to survive in a recognisable form in a non-literate culture for 1500 years.
Even if you have a genuinely ancient figure, that the stories about them are authentically 'pagan' rather than folk-Christian from the early Modern period is hard to demonstrate.
For example the Perchta (also associated with Frau Holle):
Which bring us to the intractable problem, while it is possible that such stories reflect a pre-christian past, there is usually no actual evidence for this, and assuming it to be the case is based on a failure to understand medieval and renaissance folk-Christianity.
So you do not think that known Germanic/Norse ideas including magical reindeer (deer recorded in Irish and Norse mythology including stories associated with King Author, Placing the location in area most associated with snow associated with Frau Holle - the north pole, Santa being helped by elves which are clear Germanic origin (unless you have some sources that St, Nicolas used elves to make the presents), Watching children throughout the year to see if they were naughty or nice (unless St. Nicolas recorded this is what he did). Rewarding the good and giving a negative reward to those who were bad?
Most of these are the literary creations of various 19th C individuals that have been amalgamated into modern culture.
Look at a major artistic work and read literary criticism of it, everyone insists there is some different meaning behind the text: "well Shakespeare is obviously alluding to..."
Find one where the author has commented on it and you see them reject most of these supposed 'meanings' as pure fantasy where the critic is projecting their own desires onto the text.
It's a bit like claiming Harry Potter was 'pagan' because it has elves and goblins in it, and that JK Rowling was using consciously using pagan symbology rather than common Western cultural tropes.
Do you have any evidence that these are genuinely old traditions, rather than 19th C imaginations and projections (or 18th, 17th, 16th C imaginations)?