Learn Hardcore Russian: Если на улице холодно, возьми свитер с собой. - If it is cold outside, take a sweater with you.

In Russian, a comma is normally used between the если-clause (the condition) and the main clause (the result/action).
So Если на улице холодно, ... (If it’s cold outside, …) is separated from возьми... (take…).

What part of speech is холодно here, and why isn’t it холодный?

Холодно is a “category of state” word (often treated like an impersonal predicative/adverb) used in sentences like холодно / жарко / темно.
It describes the general situation (“it’s cold”), not a noun.
Холодный is an adjective and would need a noun to agree with, e.g. холодная погода (cold weather) or холодный воздух (cold air).

Why does Russian say на улице холодно instead of a direct “it is cold outside”?

Russian often expresses “it is X” with an impersonal structure: (где?) + холодно.
На улице холодно literally means “On the street it’s cold,” i.e., “Outside it’s cold.”

What case is на улице and why?

На улице is prepositional case after на when it means location (“on/in/at”).

улица → prepositional улице
So на улице = “outside / in the street (area).”
(Compare movement: на улицу = “to the street,” accusative.)

Why is it возьми and not бери?

Both are imperatives of брать/взять (“to take”), but they differ by aspect:

возьми = perfective imperative (take it once, achieve the result) → typical for a single, concrete action.
бери = imperfective imperative (take in general / start taking / take repeatedly), which can sound like an ongoing instruction or a habitual one depending on context.

In this sentence, the intended meaning is “(Go ahead and) take a sweater with you (this time),” so возьми is natural.

Is возьми informal? How do I make it polite?

Yes, возьми is the singular informal imperative (to a friend, child, someone you address as ты).
Polite/plural form: возьмите (to вы, or to multiple people).
So: Если на улице холодно, возьмите свитер с собой.

What case is свитер in, and why does it look the same as the dictionary form?

Свитер is the direct object of возьми, so it’s in the accusative case.
For many masculine inanimate nouns, the accusative equals the nominative:

nominative: свитер
accusative: свитер

(If it were animate, it would often match genitive, e.g. возьми кота.)

What does с собой mean grammatically, and why isn’t it с тебя/с вами?

С собой means “with oneself / with you” and is the fixed expression used after verbs like “take” or “bring” to mean “along.”

с requires instrumental case
собой is instrumental of себя (reflexive “oneself”)

It stays с собой regardless of who is being addressed:

(ты) возьми с собой
(вы) возьмите с собой
(он) взял с собой

You don’t normally replace it with с тобой/с вами here, because the meaning is “take it along (with yourself),” not “take it together with you as a companion.”

Can the word order change? For example, Если на улице холодно, возьми с собой свитер.

Yes. Word order is flexible, and your version is also natural.
Common options:

Если на улице холодно, возьми свитер с собой.
Если на улице холодно, возьми с собой свитер.
Возьми свитер с собой, если на улице холодно.

The differences are mostly about emphasis and style, not basic meaning.

Why is it present tense холодно and not future будет холодно?

Both are possible, depending on context:

Если на улице холодно, ... = “If it’s cold (right now / in general when you check), …”
Если на улице будет холодно, ... = “If it will be cold (later), …”

If you’re deciding before going out and thinking about later conditions, будет холодно is often more precise.

How do I pronounce and stress the key words?

Main stresses:

Е́сли (YE-sli)
на ули́це (oo-LEE-tse)
холо́дно (ha-LOHD-na)
возьми́ (vaz-MEE)
сви́тер (SVEE-ter)
с собо́й (sa-ba-BOY)