Himininn er skýjaður í dag.

Because -inn is the suffixed definite article in Icelandic.

• himinn = sky
• himininn = the sky

So Icelandic usually puts the at the end of the noun instead of using a separate word like English does. In this sentence, the speaker is talking about the specific sky above us, so the definite form is natural.

It is nominative singular masculine, because it is the subject of the sentence.

In Himininn er skýjaður í dag, the structure is:

• Himininn = subject
• er = is
• skýjaður = predicate adjective
• í dag = today

A useful thing to know: sometimes Icelandic noun forms can look the same in more than one case, so you often identify the case from the word’s job in the sentence, not just from the ending.

Because it agrees with himininn, which is masculine singular nominative.

Icelandic adjectives must agree with the noun they describe in:

• gender
• number
• case

So here:

• himininn = masculine, singular, nominative
• skýjaður = masculine, singular, nominative

That is why you get skýjaður.

This is a very common question.

After the verb að vera (to be), Icelandic usually uses the strong adjective form in predicate position. So:

• Himininn er skýjaður = The sky is cloudy

But when an adjective comes directly before a definite noun, you usually get the weak form:

• skýjaði himininn = the cloudy sky

So:

• er skýjaður = predicate adjective → strong form
• skýjaði himininn = attributive adjective before definite noun → weak form

Yes. ský means cloud, and skýjaður means cloudy or cloud-covered.

So this is a useful vocabulary connection:

• ský = cloud
• skýjaður = cloudy

Not every Icelandic adjective is completely transparent in formation, but in this case the connection is clear and helpful for learning.

í dag is the normal Icelandic expression for today.

Literally, it is made of:

• í = in
• dag = accusative singular of dagur (day)

So learners usually just memorize í dag as a fixed expression meaning today.

Even though the literal pieces are understandable, the whole phrase functions like a time adverb in English.

Yes, absolutely.

Both of these are correct:

• Himininn er skýjaður í dag.
• Í dag er himininn skýjaður.

The difference is mainly focus:

• Himininn er skýjaður í dag starts with the sky
• Í dag er himininn skýjaður starts with today

This kind of word order change is very normal in Icelandic. In a main clause, the finite verb usually stays in the second position.

Yes, and that is actually a very common way to talk about the weather.

• Það er skýjað í dag. = It is cloudy today.
• Himininn er skýjaður í dag. = The sky is cloudy today.

The difference is:

• Það er skýjað is an impersonal weather expression
• Himininn er skýjaður talks directly about the sky

Also notice the adjective form changes:

• skýjað in Það er skýjað
• skýjaður in Himininn er skýjaður

That is because in the first sentence there is no masculine noun like himininn for the adjective to agree with.