Learn Hardcore Polish: Dzisiaj jest mi zimno, chociaż w domu jest ciepło. - Today I feel cold, although it is warm at home.

jest mi zimno is an impersonal construction: literally “it is cold to me”.
jestem zimny literally means “I am cold (to the touch)” – like a cold object or a corpse. It describes your physical temperature as an object, not your feeling.

So:

Dzisiaj jest mi zimno. = Today I feel cold.
On jest zimny. = He is cold (his body/object is cold; or metaphorically, he is cold as a person).

What is mi here? Which case is it, and why is it used?

Mi is the dative form of ja (I). It corresponds to “to me”.

Case: dative (komu? czemu? – “to whom? to what?”).
Construction: jest zimno komuś = “it is cold to someone”.

So:

jest mi zimno = it is cold to me
jest ci zimno = it is cold to you (singular, informal)
jest mu zimno = it is cold to him

Polish often uses the dative to show who is experiencing a state or feeling in these impersonal sentences (zimno, gorąco, smutno, wesoło, etc.).

Can I use mnie instead of mi in jest mi zimno?

Both mi and mnie are dative forms of ja, but they are used slightly differently.

mi is the usual, weak/clitic form, very common in speech:
- Dzisiaj jest mi zimno. – the most natural version.
mnie is the stressed/emphatic form, used for contrast or strong emphasis:
- Mnie jest zimno, a jemu nie. – I am cold, but he isn’t.

So you normally say jest mi zimno, and use mnie only if you really want to stress me.

What exactly are zimno and ciepło here – adjectives or adverbs?

In jest mi zimno and w domu jest ciepło, zimno and ciepło are adverbial (neuter) forms of adjectives used in an impersonal way.

Base adjectives: zimny (cold), ciepły (warm).
Adverb/impersonal forms: zimno, ciepło.

They function like English “it is cold/warm”:

Na dworze jest zimno. – It’s cold outside.
W domu jest ciepło. – It’s warm at home.

They do not agree in gender with the person; they are just general descriptions of the temperature.

Why is the verb jest used twice? Can I drop it, like in other Polish sentences?

Polish often drops jest in the 3rd person present (on/ona/ono):

W domu ciepło. instead of W domu jest ciepło.
Na zewnątrz zimno. instead of Na zewnątrz jest zimno.

In your sentence:

Dzisiaj jest mi zimno, chociaż w domu jest ciepło.

You can say more colloquially:

Dzisiaj mi zimno, chociaż w domu ciepło.

All of these are correct; including jest sounds a bit more neutral/standard, while dropping it can sound more spoken and elliptical. It’s less common to drop jest before mi, but Dzisiaj mi zimno is still fine.

Can I change the word order, e.g. Mi jest dzisiaj zimno or Ciepło jest w domu? Does it change the meaning?

Yes, Polish word order is flexible, and different orders change the focus/emphasis, not the basic meaning.

Examples:

Dzisiaj jest mi zimno. – neutral: “Today I feel cold.”
Mi jest dzisiaj zimno. – emphasizes me: I’m the one who is cold (maybe others are not).
Dzisiaj mi jest zimno. – emphasizes today vs other days.

For the second part:

W domu jest ciepło. – neutral.
Ciepło jest w domu. – contrastive: it’s at home that it’s warm (maybe not outside).
W domu ciepło. – shortened, typical spoken style.

All are grammatical; context decides which sounds most natural.

What does chociaż mean here, and how is it different from ale or mimo że?

Chociaż means “although / even though” and introduces a contrastive subordinate clause.

Dzisiaj jest mi zimno, chociaż w domu jest ciepło.
= Today I feel cold, although it is warm at home.

Differences:

ale = but; it usually starts a new main clause:
- Dzisiaj jest mi zimno, ale w domu jest ciepło.
  (Two separate facts: I’m cold, but the house is warm.)
chociaż / choć = although; it introduces a dependent clause explaining the surprising contrast.
mimo że = despite the fact that; similar to chociaż, but sounds a bit stronger/more explicit:
- Dzisiaj jest mi zimno, mimo że w domu jest ciepło.

In everyday speech chociaż and choć are very common; mimo że feels slightly more formal or emphatic.

Why is there a comma before chociaż?

In Polish, you normally place a comma before conjunctions that introduce a subordinate clause, such as chociaż, że, ponieważ, kiedy.

..., chociaż w domu jest ciepło.

Here “chociaż w domu jest ciepło” is a dependent (subordinate) clause explaining the contrast, so it must be separated by a comma from the main clause “Dzisiaj jest mi zimno”.

Can I use choć instead of chociaż? Is there a difference?

Yes, you can:

Dzisiaj jest mi zimno, choć w domu jest ciepło.

Choć is essentially a shorter, slightly more colloquial form of chociaż in this meaning (although). In this sentence, they are interchangeable and the meaning remains the same.

There is also a different use of choć meaning “at least / even / come on” in some contexts, but here it’s just “although”.

What is the role of dzisiaj here, and can I use dziś instead? Where can I place it?

Dzisiaj means “today”. Dziś is a shorter, slightly more formal/literary but very common variant; they are interchangeable in meaning.

You can say:

Dzisiaj jest mi zimno, chociaż w domu jest ciepło.
Dziś jest mi zimno, chociaż w domu jest ciepło.

Placement is flexible:

Dzisiaj jest mi zimno... (most neutral)
Jest mi dzisiaj zimno... (focus on today)
Jest mi zimno dzisiaj... (often contrast with other days: “I’m cold today, unlike before.”)

All are grammatical; the difference is mostly emphasis and rhythm.

What does w domu literally mean, and which case is used? How is it different from do domu or z domu?

W domu = “in/at home”, using:

Preposition w (in),
plus the locative case of dom: dom → w domu.

Contrast:

w domu – in/at home (location, where?):
- W domu jest ciepło. – It’s warm at home.
do domu – to home (direction, where to?):
- Idę do domu. – I’m going home.
z domu – from home (from where?):
- Wyszedłem z domu. – I left home.

So in your sentence we talk about the state of temperature at a location, so w domu (locative) is required.

How would I make this sentence negative? Where does nie go?

To negate this kind of sentence, nie goes before the verb jest:

Dzisiaj nie jest mi zimno, chociaż w domu jest ciepło.
= Today I am not cold, although it is warm at home.

You cannot say:

*Dzisiaj jest nie mi zimno – incorrect.
*Dzisiaj jest mi nie zimno – also incorrect.

If you drop jest, you usually keep it positive; the negative version sounds better with jest present:

Positive spoken: Dzisiaj mi zimno.
Negative: Dzisiaj nie jest mi zimno.

How do you pronounce dzisiaj and chociaż?

Approximate pronunciations:

dzisiaj: /ˈd͡ʑi.ʂaj/ (in careful speech) or /ˈd͡ʑi.saj/
- dź / d͡ʑ – like “j” in “jeans”, but softer.
- si before a vowel becomes a soft ś sound.
  So it’s roughly like “JEE-shay” or “JEE-say” (but with a softer sh/s).
chociaż: /ˈxɔ.t͡ɕaʂ/
- ch – like German “Bach” (voiceless velar fricative).
- ci / ć / t͡ɕ – a soft “tch” sound, like a very soft “ch” in “cheeks”.
- Final -sz / -ś / -ż / -cz-type sounds are pronounced clearly; -aż here is like “ash” but with the sh further back.

Very rough English approximations:

dzisiaj ≈ “JEE-shy”
chociaż ≈ “HO-tyash” (with the h like in “Bach”, not English “home”).