Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Youthful, Dry
Milne maintains a light and carefree tone throughout his stories, even when the characters are in dire circumstances. Remember how it was funny when Piglet met a Heffalump, even though our dear friend was terrified? That's because Milne creates dry humor through irony—particularly dramatic irony.
Even though the narrator is "omniscient" (take a look at the "Narrator Point of View" section for more detail) in that he can see the perspective of all the characters, he is also limited in that he assumes the perspective of the characters. In this way, Milne's tone is also very youthful, almost naïve.
For instance, Milne describes how Pooh falls into the deep pit. "Pooh was so busy not looking where he was going that he stepped on a piece of the Forest which had been left out by mistake" (House.3.31). Milne assumes that Pooh's "not looking where he was going" is intentional, as Pooh is "busy" with it. And the "piece of the Forest" is clearly in the wrong place, left by some mysteriously thoughtless third party.
You see, being childlike, Milne's characters tend to be a little bit egocentric. So when Milne adopts their perspectives, he ends up narrating the world from their point of view too. Even though we, the audience, see through Owl's feigned intelligence, our narrator accepts the characters' belief that Owl is wise, taking his word for the idea that "Contradiction" in the opposite of "Introduction" (House.Contradiction.1)
This allows Milne to write dryly, in spite of all the absurdity that occurs. For example, only through Christopher Robin's perspective does he ever state that Pooh is silly or ignorant. For the rest, he accepts Pooh's twisted logic as completely reasonable. This dry tone is what probably makes adults appreciate these stories as much as kids.