På mörka morgnar tar barnen på sig en reflex och regnbyxor innan de går ut.

Because Swedish often uses på in time expressions like på morgonen for in the morning. In this sentence, på mörka morgnar means on dark mornings or on mornings when it is dark.

Also, morgon has the plural morgnar, so:

• en morgon = a morning
• morgnar = mornings

The adjective has to agree with the noun.

Here, morgnar is plural, so the adjective takes the plural form mörka.

Compare:

• en mörk morgon = a dark morning
• ett mörkt rum = a dark room
• mörka morgnar = dark mornings

So mörka is there because morgnar is plural.

This is because Swedish follows the V2 rule in main clauses: the finite verb usually comes in the second position.

Here, På mörka morgnar comes first as a time expression, so the verb tar must come next:

• På mörka morgnar tar barnen på sig...

If the subject came first, you would get:

• Barnen tar på sig... på mörka morgnar

Both are grammatical, but once På mörka morgnar is moved to the front, tar has to stay in second position.

Ta på sig means to put on when talking about clothes or something worn on the body.

So:

• barnen tar på sig en reflex och regnbyxor
  = the children put on a reflector and rain pants

It is a very common Swedish expression.

Because ta på sig is a multi-word verb, and in a normal sentence the finite verb often stands earlier while the other parts stay later.

So the full verb is:

• ta på sig

But in the sentence it appears as:

• tar barnen på sig

This is normal in Swedish.

Compare:

• att ta på sig regnbyxor = to put on rain pants
• barnen tar på sig regnbyxor = the children put on rain pants

Sig is the reflexive pronoun for the third person. Here it means themselves.

So barnen tar på sig literally means something like:

• the children put on themselves

Natural English does not say it that way, but Swedish uses sig in this expression.

The same sig can also mean himself, herself, itself, or themselves, depending on who it refers to.

Barnen is the definite plural form, meaning the children.

Useful forms are:

• ett barn = a child
• barn = children
• barnet = the child
• barnen = the children

So barn is unusual because the indefinite singular and indefinite plural look different only through context:

• ett barn = one child
• två barn = two children

In your sentence, barnen is used because it means the children, not just children in general.

Not in the English sense. In Swedish, en reflex usually means a reflective safety item worn so that people can see you in the dark, especially children.

So here it means something like:

• a reflector
• a reflective tag
• a reflective item

It is a common everyday Swedish word, especially in discussions about road safety and children.

Because regnbyxor is plural and indefinite.

In Swedish, indefinite plural nouns usually do not take an article.

Compare:

• en reflex = a reflector
• regnbyxor = rain pants

You would only add a definite ending if you meant the rain pants:

• regnbyxorna = the rain pants

Also, byxor is normally a plural word in Swedish, just like pants or trousers in English.

Because innan introduces a subordinate clause, and subordinate clauses do not use the main-clause V2 word order.

So after innan, the normal order is:

• de går ut = they go out

That gives:

• innan de går ut = before they go out

If it were a main clause with something placed first, then V2 would apply:

• Nu går de ut = now they are going out

But after innan, Swedish keeps the subject before the verb.

Gå ut means go out or go outside.

In this sentence, it clearly means go outside.

Like ta på sig, this is also a multi-word verb:

• gå ut = to go out
• de går ut = they go out

So the whole ending innan de går ut means before they go outside.