Learn Hardcore German: Wenn dir kalt ist, kannst du meinen Pullover anziehen. - If you are cold, you can put on my sweater.

dir kalt ist = to you it is cold → “you are (feel) cold”
du kalt bist would literally be “you are cold” in the sense of having a cold personality or a low body temperature as an objective fact, which is not how you usually talk about feeling cold.

So Wenn dir kalt ist is the natural idiomatic way to say “If you’re cold” in German.

Why is it dir and not dich in Wenn dir kalt ist?

dir is the dative form of du. The pattern jemandem ist kalt always uses the dative:

mir ist kalt (to me it is cold)
dir ist kalt (to you it is cold)
ihm / ihr ist kalt (to him / her it is cold)
uns ist kalt (to us it is cold)
euch ist kalt (to you all it is cold)
ihnen / Ihnen ist kalt (to them / to you formal it is cold)

dich is the accusative form and is used as a direct object (e.g. Ich sehe dich – “I see you”), but “being cold” is not treated like a direct object in German; it’s more like an experience that happens to someone, so German uses the dative.

Could you also say Wenn es dir kalt ist? Is es missing here?

You could say Wenn es dir kalt ist, but in everyday speech people normally drop es and just say Wenn dir kalt ist.

The full underlying structure is “Es ist dir kalt” (literally: It is cold to you), with es as a dummy subject. In colloquial German this es is often omitted in sentences like this, especially when there’s another short element in the “first position” (here: dir). Both versions are grammatically acceptable; the shorter one is just more natural here.

Why does the verb ist go at the end in Wenn dir kalt ist?

Wenn introduces a subordinate clause in German. In such clauses, the conjugated verb goes to the end of the clause:

main clause: Dir ist kalt. (verb in second position)
subordinate clause: ..., weil dir kalt ist. (verb at the end)
Wenn dir kalt ist, ... (same pattern)

This verb-at-the-end rule applies with many conjunctions that introduce subordinate clauses, such as weil, dass, obwohl, wenn, etc. So Wenn dir kalt ist is the correct word order; Wenn dir ist kalt is wrong.

Why is the order kannst du and not du kannst in the second part: ..., kannst du meinen Pullover anziehen?

In a main clause, German usually wants the finite verb (here kannst) in second position. When a subordinate clause (like Wenn dir kalt ist) comes first, that entire clause counts as the “first element” of the sentence. The finite verb of the main clause must then come immediately after it:

Neutral order: Du kannst meinen Pullover anziehen.
With wenn-clause first: Wenn dir kalt ist, kannst du meinen Pullover anziehen.

So the comma ends the subordinate clause; then the main clause starts, and the finite verb kannst must come first in that main clause, before the subject du.

What is happening with kannst … anziehen? Why is anziehen at the end?

anziehen is a separable verb: anziehen = an (prefix) + ziehen (verb). On its own in the present tense it splits:

Du ziehst den Pullover an.

But when you add a modal verb like können, the structure changes:

The modal verb (here kannst) is conjugated and takes the normal verb position (second in a main clause).
The full infinitive anziehen stays together and goes to the end of the clause.

So:

with no modal: Du ziehst meinen Pullover an.
with modal: Du kannst meinen Pullover anziehen.
with wenn-clause fronted: Wenn dir kalt ist, kannst du meinen Pullover anziehen.

That’s why anziehen appears at the very end.

Why is it meinen Pullover and not mein Pullover?

Pullover is a masculine noun: der Pullover.

In the sentence, Pullover is the direct object of anziehen (what are you putting on?). Direct objects take the accusative case. For masculine nouns, the possessive determiner mein changes in the accusative:

nominative: mein Pullover (as subject) – Mein Pullover ist blau.
accusative: meinen Pullover (as object) – Ich ziehe meinen Pullover an.

So meinen Pullover is correct here because it’s the masculine accusative form.

What does Pullover exactly mean, and are there other words I could use?

der Pullover is a general word for a sweater / jumper (thing you pull over your head).

Common alternatives:

der Pulli – short, informal version of Pullover
der Sweater – used, but less common; more English-influenced
der Hoodie – for a hooded sweatshirt (informal, from English)
der Strickpullover – knitted sweater (more specific)

In this neutral context, Pullover or Pulli are both normal.

Could you also say Wenn du frierst, kannst du meinen Pullover anziehen? Is there a difference from Wenn dir kalt ist?

Yes, Wenn du frierst, kannst du meinen Pullover anziehen is correct and quite natural.

Nuance:

dir kalt sein focuses on the state: “you are (feel) cold”.
frieren focuses a bit more on the physical process of shivering/feeling chilly, often slightly stronger.

In everyday use, they’re very close in meaning. Both are fine; Wenn dir kalt ist is a bit more neutral and common.

Why is it kannst du and not darfst du or sollst du? What would those mean?

Modal verbs here express different nuances:

kannst du – “you can / are able to / are free to” → offers an option, friendly and neutral.
darfst du – “you may / are allowed to” → stresses permission, e.g. Wenn dir kalt ist, darfst du meinen Pullover anziehen sounds like: I allow you to wear it.
sollst du – “you should” → more of a recommendation or mild instruction: Wenn dir kalt ist, sollst du meinen Pullover anziehen = “If you’re cold, you should put on my sweater.”

In the original sentence, kannst du is used because the speaker is just offering their sweater as a possibility, not commanding or formally granting permission.

What’s the difference between wenn, wann, and falls in this type of sentence?

In this context:

wenn = “if / whenever” (conditional or repeated situation)
Wenn dir kalt ist, kannst du meinen Pullover anziehen.
wann asks about time (“when?”) and is not used for conditions like this:
Wann ist dir kalt? – “When are you (usually) cold?”
falls can also mean “if”, usually a bit more hypothetical or formal: Falls dir kalt ist, kannst du meinen Pullover anziehen.
→ slightly more like “in case you’re cold”.

So for the original sentence, wenn is the standard, natural choice.

How would I say this politely to a stranger, not using du?

Use the formal Sie and its dative Ihnen:

Wenn Ihnen kalt ist, können Sie meinen Pullover anziehen.

Forms:

dir → Ihnen (dative of Sie)
du kannst → Sie können

Everything else stays the same.

Why is there a comma between Wenn dir kalt ist and kannst du meinen Pullover anziehen?

In German, a subordinate clause (introduced by words like wenn, weil, dass, etc.) must be separated from the main clause by a comma.

So:

Wenn dir kalt ist, = subordinate clause
kannst du meinen Pullover anziehen. = main clause

The comma is obligatory here; you cannot omit it in correct written German.