Bind dit tørklæde, før du går ud i kulden!

Because tørklæde is a neuter noun in Danish: et tørklæde.

Danish possessives change to match the noun:

• din
  • common gender (en-word)
• dit
  • neuter (et-word)
• dine
  • plural

So:

• en jakke → din jakke
• et tørklæde → dit tørklæde
• dine handsker → dine handsker

Bind is the imperative form of at binde.

The imperative is used for commands, instructions, or advice:

• Bind dit tørklæde! = Tie your scarf!
• Kom her! = Come here!
• Spis nu! = Eat now!

In Danish, the subject du is usually left out in commands, just like in English.

Because før introduces a subordinate clause.

In Danish, main clauses usually follow the V2 rule: the finite verb comes second. But in subordinate clauses, the verb normally comes after the subject.

So:

• main clause: du går
• after før: før du går

That is why the sentence has:

• før du går ud i kulden

not:

• før går du ud i kulden

Går ud means go out or go outside.

This is a very common Danish verb + particle combination:

• gå ud = go out
• gå ind = go in
• komme hjem = come home
• tage af = take off

So in this sentence:

• du går ud i kulden = you go out into the cold

The ud adds the idea of moving from inside to outside.

This is idiomatic Danish.

Danish often uses the definite form in weather and environment expressions:

• i solen = in the sun
• i regnen = in the rain
• i vinden = in the wind
• i kulden = in the cold

So i kulden does not necessarily mean a specific, literal the cold. It is just the natural Danish way to say in/into the cold.

Yes. At binde means to tie.

So Bind dit tørklæde suggests fastening or wrapping the scarf properly, not just putting it on loosely.

A slightly different sentence would be:

• Tag dit tørklæde på = Put your scarf on

The difference is:

• bind = tie it
• tag ... på = put it on

Because Danish forms many nouns as compounds.

Tørklæde is a single compound noun meaning scarf. Danish often writes such combinations as one word, where English might use one word, two words, or a hyphen depending on the case.

This is very common in Danish:

• hoveddør = front door
• sommerferie = summer holiday
• regnjakke = rain jacket

So tørklæde is just the normal written form.

You could, but the meaning shifts a little.

• gå ud i kulden = go out into the cold
  This emphasizes leaving the inside and going outside.

• gå i kulden = walk/be in the cold
  This can sound more like being out there already, or moving around in the cold.

In this sentence, gå ud i kulden is the most natural choice because it describes going outside.

Because før du går ud i kulden is a subordinate clause, and many Danish writers put a comma before such clauses.

You may also see variation depending on comma style:

• traditional comma: Bind dit tørklæde, før du går ud i kulden!
• new comma: Bind dit tørklæde før du går ud i kulden!

So the comma is not about meaning here; it is mainly about spelling/punctuation convention.

The hardest words are probably tørklæde, går, and kulden.

A rough guide for English speakers:

• bind: sounds a bit like bin with a softer Danish d
• dit: roughly dit
• tørklæde: tricky; the first part has a rounded vowel not found in English
• før: roughly like fur but with rounded lips
• går: not like English gore, but somewhat in that direction
• kulden: roughly kool-den, though the Danish u is not exactly English oo

The biggest challenge is usually the vowels, especially ø in før and tør-. If you want, I can also break the whole sentence down into a more detailed pronunciation guide.