I see also that the theories about Santa Claus's identity are equally as varied as the ones about Mr. Hat & Cloak. My take on this is similar to my take on H&C: we're meant to understand that Santa Claus is simply Dumbledore.

• Santa Claus had possession of the Cloak of Invisibility and passed it down to Harry, who Santa somehow knew was its rightful heir.
• Santa Claus also somehow knows about the full misdeeds of James Potter, many of which are known to no one else.
• Santa Claus has the political and magical power to create Portkeys on the Hogwarts grounds and get away with it.
• Santa Claus has deep insight into Dumbledore's true motives, and makes true statements about him without ever stating that Dumbledore is a different person.
• Santa Claus knows little about Quirrell, but doesn't trust him.
• Santa Claus says that he cares about Harry Potter's well being and wants him to be more careful in the future.

The only person we know for whom all the above facts are true is Dumbledore.

However, the "S" who left notes for Hermione is not Santa Claus. It's Severus Snape, who we know for a fact was the mysterious person helping SPHEW in its mission. The two signatures happen to both begin with S, but that's a coincidence; if the writer had intended Harry and Hermione to figure out that the two note senders were the same, they would have signed the letters to Hermione "Santa Claus" or at least "SC". Therefore, "S" doesn't know about the first notes and was not trying to connect his notes to them.

Let me add to my previous hypotheses about Eliezer's state of mind while writing: The fact that something is entirely mysterious to the characters does not mean that it's supposed to be entirely mysterious to us. We are certainly meant to know that "S" is Snape. We know this because of Interlude with the Confessor. It could not be any more blatant without being stated in the Author's Notes.

I equally believe that we're meant to know that "Santa Claus" is Dumbledore. Everything in the Santa Claus notes is entirely 100% consistent with what we know of Dumbledore and his character from canon and from MoR. Likewise, the fact that Mr. Hat and Cloak is entirely mysterious to Zabini and Hermione does not mean that we are supposed to reach deep into the implausible for explanations.

Certainly I could be wrong about any of this. The simple answer is not always the best answer. But all other things being equal, it's a good bet. And the evidence for these "simple" explanations is at least equal to the evidence that, say, Hat and Cloak is a manifestation of Voldemort's essence that leaves Quirrell's body for unknown reasons.