Note: This answer pertains to Santa Claus, as distinct from St Nicholas, Sinterklaas, Krampus, etc. - as per the question.
He is not bound by GDPR.
an entity or more precisely an "enterprise" has to be engaged in "economic activity" to be covered by the GDPR
https://en.wikipedia.org/wiki/General_Data_Protection_Regulation
What qualifies as "economic activity"? I'm glad you asked:
... the Court determins that an activity is economic on the basis of two criteria of agreement and renumeration
(from https://www.springer.com/cda/content/document/cda_downloaddocument/9789462651166-c2.pdf )
I do not agree with other posts that the recipients of the gifts agree (in the legal sense, nor in any sense that would stand up in court). I am not aware of any way a person can "agree" to be the recipient of gifts from Santa (there are obvious ways to object, of course).
Santa Clause also does not seem to meet the criteria for remuneration. He brings "gifts" or "presents" (https://en.wikipedia.org/wiki/Santa_Claus); "A gift or a present is an item given to someone without the expectation of payment or return" - https://en.wikipedia.org/wiki/Gift
In many cultures, something that may be considered payment is left for Santa (e.g. milk & cookies in the US & Canada; sherry or beer and mince pies in Britain & Australia; rice porridge in Denmark, Norway & Sweden); however, I can find no source that indicates that failing to leave these items will result in suspension of gifts. - https://en.wikipedia.org/wiki/Santa_Claus
Also:
'enterprise' means a natural or legal person engaged in an economic activity, irrespective of its legal form, including partnerships or associations regularly engaged in an economic activity.
As far as I can tell, Santa Clause is neither a natural nor legal person. Human Beings "acquire legal personhood when they are born (or even before...", juridical persons "acquire legal personhood when they are incorporated" (https://en.wikipedia.org/wiki/Legal_person). I am not aware of Santa Clause having been born, nor incorporated.
Addendum:
There was a question if "being nice" qualifies as remuneration. I would argue against this for the following reasons:
- If an item is traded for remuneration, it is, by definition, not a present. The items are clearly declared as presents.
- Santa is not the recipient of the "niceness" (in almost all cases).
- Although it is clearly document in "Santa Claus is coming to town", (H. Gillespie et al.) that "he's going to find out who's been naughty or nice", "He knows when you've been bad or good" and "He's making a list", there is nothing in this thesis that claims that this list affects the presents. Wikipedia claims it does, but none of the sources it cites (that I checked) back this up. Does anybody know of a reasonable source for this, or is it just an urban myth? Does anybody know of a child that has not received a present, because they were naughty?