Ég set húfuna á mig þegar það er rok.

Set is the 1st person singular present tense of setja.

So:

• ég set = I put / I place
• in this sentence, ég set húfuna á mig means I put the hat on myself, which in natural English is I put on my hat

With clothes, Icelandic often uses setja ... á sig/mig/þig for put on.

Because húfuna is the direct object of the verb set, so it appears in the accusative case.

The basic noun is:

• húfa = a hat, a cap

Here you need the definite singular accusative form:

• húfuna = the hat

A useful comparison:

• húfa = a hat
• húfan = the hat, nominative
• húfuna = the hat, accusative

So the sentence uses húfuna because it is the thing being put on.

Because Icelandic uses different cases after á depending on whether there is movement or location.

• á + accusative = movement onto something
• á + dative = being on something, location

So:

• á mig = onto me
• á mér = on me

In this sentence, the hat is being moved onto the speaker, so á mig is correct:

• Ég set húfuna á mig = I put the hat on me

Compare:

• Húfan er á mér = The hat is on me / I am wearing the hat

Because with clothing, body parts, and similar things, Icelandic often does not use a possessive if the owner is already obvious.

So instead of saying the equivalent of I put my hat on, Icelandic often says:

• Ég set húfuna á mig

Literally that is I put the hat on me, but naturally it means I put on my hat.

You can add a possessive for emphasis or contrast, for example:

• Ég set húfuna mína á mig = I put on my hat

But in a normal sentence, that often sounds less necessary than it would in English.

Because sig is only used as a 3rd-person reflexive pronoun.

So:

• mig = me / myself
• þig = you / yourself
• sig = himself / herself / itself / themselves

Since the subject here is ég = I, the correct form is mig:

• Ég set húfuna á mig = I put the hat on myself

If the subject were hann or hún, then sig could appear:

• Hann setur húfuna á sig = He puts the hat on himself

Literally, þegar means when.

But in a sentence like this, which describes a general habit, English often translates it more naturally as when or whenever:

• Ég set húfuna á mig þegar það er rok
  = I put on my hat when it is very windy
  = I put on my hat whenever it is very windy

So the exact English wording depends on style, but the Icelandic is perfectly normal for a repeated situation.

It is a common kind of weather expression.

• það is a dummy subject, like English it in it is raining
• er = is
• rok is a noun meaning gale, very strong wind, or severe windiness

So það er rok means something like:

• it is very windy
• there is a gale
• the wind is really strong

It is stronger than just saying there is some wind. This is not a light breeze.

It could technically be either, because the Icelandic present tense can cover both simple present and some uses that English might express differently.

But in this sentence, the most natural reading is a habitual or general one:

• I put on my hat when it’s very windy

That is because þegar það er rok sounds like a repeated condition, not just one single moment.

Yes.

The given sentence is a normal, natural order:

• Ég set húfuna á mig þegar það er rok

You can also move the þegar clause to the front:

• Þegar það er rok, set ég húfuna á mig

Notice that in the main clause, the verb comes second:

• set ég

That is part of Icelandic’s usual verb-second pattern.

You may also hear:

• Ég set á mig húfuna

This is also possible, with a slightly different rhythm or emphasis, but the original order is very straightforward for learners.

That would be a different idea.

The original sentence is about the action of putting the hat on.

If you want the state of wearing it, common Icelandic options are:

• Ég er með húfu = I am wearing a hat
• Húfan er á mér = The hat is on me

So:

• Ég set húfuna á mig = I put the hat on
• Ég er með húfu = I am wearing a hat

That is an important distinction in Icelandic.