Hvis køletasken er for tung, bærer jeg den ned til bilen.

Yes. Hvis is the normal Danish word for if in a condition.

In this sentence, Hvis køletasken er for tung sets up the condition:

• If the cooler bag is too heavy ...

So this is a straightforward if-clause.

Because Danish usually puts the definite article at the end of the noun.

So:

• en køletaske = a cooler bag
• køletasken = the cooler bag

And:

• en bil = a car
• bilen = the car

This -en ending is common for singular common-gender nouns.
So English the is often built into the noun itself in Danish.

In front of an adjective, for often means too.

So:

• for tung = too heavy
• for stor = too big
• for dyr = too expensive

This is a very common pattern in Danish.
So even though for often looks like English for, here it does not mean the same thing.

This is because Danish main clauses normally follow the verb-second rule.

The sentence begins with the if-clause:

• Hvis køletasken er for tung

That whole clause takes the first position in the sentence. After that, the finite verb of the main clause must come next:

• bærer jeg den ned til bilen

So Danish says:

• Hvis ..., bærer jeg ...

not:

• Hvis ..., jeg bærer ...

This is one of the most important word-order patterns in Danish.

Den means it here, and it refers back to køletasken.

Because køletaske is a common-gender singular noun, the matching pronoun is den.

So:

• køletasken = the cooler bag
• den = it

Danish uses:

• den for common-gender singular nouns
• det for neuter singular nouns
• de for plural nouns

The infinitive is bære, meaning to carry.

The present tense is bærer:

• jeg bærer = I carry / I am carrying
• du bærer
• han/hun bærer

Danish present tense is simple because the verb does not change for different persons the way it does in some other languages. You use the same present form for all subjects.

Literally:

• ned = down
• til = to
• bilen = the car

So ned til bilen is something like down to the car.

Danish often uses a directional word like ned, op, ind, or ud together with a verb of movement:

• gå ned = go down
• tage ned = take down
• bære ned = carry down

Then til bilen adds the destination: to the car.

So ned gives the direction, and til bilen tells you where.

Because Hvis køletasken er for tung is a subordinate clause, and it comes before the main clause.

In standard Danish writing, a comma is normally used to separate that introductory clause from the main clause:

• Hvis køletasken er for tung, bærer jeg den ned til bilen.

So the comma helps show the structure:

• condition first
• main result after

Yes, you sometimes can.

Adding så can make the result feel a bit more explicit, similar to English then:

• Hvis køletasken er for tung, så bærer jeg den ned til bilen.

That is understandable and natural in many contexts, especially in speech. But in a neutral sentence, Danish often leaves så out.

So:

• Hvis ..., bærer jeg ... = perfectly normal
• Hvis ..., så bærer jeg ... = also possible, often with a slightly more conversational or emphatic feel