I usually interpret this as the subject being so intimate with the object that they claim some metaphorical possession over it. Effectively working as a reinforcer.
Linguistics
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Imagine YouTuber describing a vintage computer: “...above the keyboard, you’ll find your cursor keys,” knowing that 99 % of their viewers never owned that type of computer.
How do you explain that case?
It still looks for me like an extension of the idea of possession to refer to closeness - as if the youtuber is talking about the cursor keys of a hypothetical computer that you'd be using. For example, note how it would sound natural if the youtuber said "above the keyboard, you'll find your cursor keys... well, one of my cursor keys is missing, but you would find it here". (imagine that the machine is in a rather poor condition), contrasting the one in his computer with yours.
You'll see this sort of extension of the role of the possessive fairly often across languages. Latin for example shows something similar:
1 Vivāmus, mea Lesbia, atque amemus, // Let us live, my Lesbia, and-also [let us] love
Focus on "mea Lesbia". Why is that "mea" (my.F.NOM) there? It doesn't indicate that Lesbia belongs to the narrator, nor that she's necessarily related to him, but instead that he holds her metaphorically close to him. Sometimes this appears with the genitive too, instead of personal pronouns, but I'm having a hard time looking for examples.
OK, I kinda get it. However, I will still be drawing a rage comic about this once I get a graphics tablet.
Rage comic idea
◰ Kid: *sings to a sing-along video on their tablet* "♪ now I know my ABCs ♫"
◳ Ghost of Karl Marx: *appears* "DON'T SAY THAT!"
Kid: *shocked*
◱ Karl Marx: *monologue all over the panel* "The modern Latin alphabet is not your private property! It is in the public domain, the collective ownership of mankind, and used by all English speakers as well as by literate people all over the world with minor variations. Billions of lives were made easier with a common writing system and a standard ordering of its glyphs. Learning what countless other children in the past few centuries have mastered does not give you the right to claim ownership of this knowledge and, in fact,..."
Kid: "Oh my god!"
◲ Karl Marx: *slaps kid with Das Kapital* ~(or~ ~maybe~ ~a~ ~better~ ~punchline,~ ~IDK)~
I see your sarcasm tag so I will take this rant as lightly as possible.
In any case, not only it's a normal turn of phrase in English, it's also relatively common in Greek. Maybe a bit less than English, but all the examples could work.
It also reminds me of a similar but not identical construction in German, where the dative personal pronoun is used to relate an event to the person's feelings and point of view, instead of objectively describing a situation.
I can understand German and my native language is Czech. Could you provide some German examples? What you described (which I imagine could be im Nebel so dick dass du deine Füße nicht sehen könntest/in fog so thick that you could not see your feet) seems like an entirely normal use of personal pronouns to me (though the generic pronoun man/one would be better to use in formal writing in the previous example, as the perspective is objective). And yes, I did not use dative but I don't think this would be bound to a specific declension form.
Could you provide some German examples?
Mir ist kalt. Sie ist mir bekannt. Mir ist dieser Preis viel zu teuer.
Draußen ist es so kalt, da frieren dir die Eier ab!
That's absolutely valid use of personal pronouns.
Mir ist kalt.
We say exactly this for “I am cold” in Czech. I have no problems with that nor your other examples, as they actually refer to the first person’s perspective. It is them who is cold and the general pronoun man would not make sense.
However, imagine a YouTuber showing off a vintage computer, saying “above the keyboard, you’ll find your cursor keys” to the audience. As a viewer who most likely does not own such a computer, in no sense of the word are the keys mine.
Oh, you are serious that you don't get this pragmatic construction. You need not to interpret this as a literally-meant possessive, because it isn't a literal possession. If you cannot do that, we aren't getting anywhere.
You need not to interpret this as a literally-meant possessive
I don’t, mir is not a possessive. The sentence could be literally translated as “For me, [it] is cold”. The feeling of cold is the speaker’s perspective expressed logically.
But why use my ABCs rather than the ABCs? The alphabet is the same for everyone, the feeling of cold in a location is not.