Learn Hardcore Turkish: Taş soğuk.

Turkish typically drops the present‐tense copula (the equivalent of “is/are”) in simple nominal sentences. So instead of saying Taş soğuk’tur, you just say Taş soğuk and it naturally means “The stone is cold” or “It’s stone-cold.”

What’s the literal word order here? Isn’t it usually adjective + noun in English?

Yes, in English we say “cold stone,” but in Turkish this is literally “stone cold.” The noun taş comes first (nominative, unmarked), then the adjective soğuk. Noun + adjective order is quite common in predicative (copula‐less) statements.

Is Taş soğuk an idiom like “stone-cold” in English, or is it just describing an actual stone?

It can be both. Literally, Taş soğuk means “the stone is cold.” Idiomatically, you can use it just as in English—to say something is “bone-chilling” or “freezing,” even if it isn’t a stone (e.g. “Bu su taş soğuk!” = “This water is stone-cold!”).

Why doesn’t taş take a case ending here? Shouldn’t it be in the nominative or something else?

It is already in the nominative (the default, unmarked form). Subjects and predicate nouns in such copula‐less sentences remain unmarked. Only objects, indirect objects, or possessives get specific case or possessive endings.

How would I negate it? How do I say “The stone is not cold”?

You attach the negation -değil after the adjective:
Taş soğuk değil.
Literally “Stone cold not,” i.e. “The stone isn’t cold.”

How can I emphasize that it’s extremely cold, like “really stone-cold”?

You can either drop the “stone” metaphor and say Çok soğuk (“very cold”), or keep the metaphor and say Tam taş gibi soğuk / Resmen taş gibi soğuk (“literally/absolutely stone-cold”).

What if I wanted the very formal or written version with the copula shown?

You’d add the copula suffix -tur (a variant of -dır/dir for 3rd person):
Taş soğuktur.
That reads as “It is stone-cold” in a more formal or dictionary style.

How do I turn it into a question like “Is the stone cold?”

Simply add the question particle -mu (with vowel harmony) after the adjective:
Taş soğuk mu?
= “Is (the) stone cold?”

And what about plural? How would I say “The stones are cold”?

Pluralize the noun with -lar/-ler (here taş → taşlar) and keep the same structure:
Taşlar soğuk.
= “Stones are cold.”