Á nóttunni kemur oft frost, en um hádegið bráðnar það af rúðunum.

These are two different time expressions:

• á nóttunni = at night / during the night
• um hádegið = around noon / at midday

The prepositions are not interchangeable here. Icelandic often uses fixed prepositional phrases for time, so it is best to learn them as whole chunks.

Nóttunni is the dative singular definite form of nótt (night).

So:

• nótt = night
• nóttin = the night
• nóttunni = to/in/on the night, after a preposition that takes dative here

In á nóttunni, the phrase is idiomatic and means at night or during the night.

Hádegið is the accusative singular definite form of hádegi (midday, noon).

Here it appears after um, which takes the accusative in this expression:

• hádegi = midday
• hádegið = the midday / noon

So um hádegið means around noon or at midday.

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

So in:

• Á nóttunni = first element
• kemur = second element
• frost = subject, after the verb

If you started with the subject instead, you could say:

• Frost kemur oft á nóttunni.

Both are grammatical, but the original sentence emphasizes the time phrase first.

Literally, it means frost comes.

But in natural English, that usually becomes something like:

• there is frost
• frost forms
• it freezes

Icelandic often uses verbs like koma (come) in ways that sound more concrete than English.

Because the verb has to stay in second position, adverbs like oft (often) commonly come after the finite verb.

So:

• Á nóttunni kemur oft frost

is a normal Icelandic order.

English speakers often expect the subject to come earlier, but in Icelandic the V2 rule is stronger.

Það refers back to frost.

That is why it is neuter singular:

• frost is a neuter singular noun
• það is the matching pronoun for a neuter singular noun

So bráðnar það means it melts, where it = the frost.

Because bráðna means to melt intransitively — that is, something melts by itself.

• bráðna = melt
• bræða = melt something

So:

• Frostið bráðnar = The frost melts
• Sólin bræðir frostið = The sun melts the frost

In your sentence, the frost is melting on its own, so bráðnar is the correct form.

Because af means off / from, and here it shows that the frost melts off the windows.

Also, af takes the dative, so rúðunum is in the dative plural.

• rúða = pane / window
• rúðurnar = the panes / the windows
• rúðunum = off/from the panes/windows

So af rúðunum = off the windows.

Because Icelandic often talks about windows/panes in the plural in this kind of context.

So the image is that frost has formed on the window panes and later melts off them.

If you were talking about only one pane, you could use singular:

• af rúðunni = off the window/pane

Because frost here is being talked about as a general weather phenomenon, not as one specific, already-identified frost.

By contrast, definite forms are common in Icelandic:

• in fixed time expressions, like á nóttunni and um hádegið
• when referring to understood objects, like rúðunum

English and Icelandic do not always use definiteness in the same way, so this is something learners usually need to get used to.

The present tense is being used for a habitual or general situation:

• At night frost often comes/forms
• around midday it melts off the windows

This is very similar to English, where the present tense can also describe regular or typical events.