Hún segir að svefnpokinn hennar sé hlýrri en minn, svo henni verður ekki kalt í nótt.

Here að means that. It introduces the clause after segir:

• Hún segir að ... = She says that ...

It is a very common way to introduce reported speech or reported information in Icelandic.

Sé is the present subjunctive form of vera (to be).

In a sentence like this, Icelandic often uses the subjunctive after verbs like segja when reporting what someone says, thinks, or claims:

• Hún segir að ... sé ... = She says that ... is ...

This can make the clause feel more like reported information rather than a plain fact stated by the speaker. You may also see er in some contexts, but sé is very natural here.

Because að introduces a subordinate clause.

In main clauses, Icelandic often follows verb-second word order. But in subordinate clauses introduced by words like að, the order is usually more like:

• subject + verb

So this is normal:

• að svefnpokinn hennar sé hlýrri ...

not a verb-second pattern.

The usual Icelandic pattern for possession is:

• noun + possessive

So:

• svefnpokinn hennar = her sleeping bag
• bíllinn minn = my car
• húsið okkar = our house

This is one of the first word-order differences English speakers notice in Icelandic.

The ending -inn is the definite article, attached to the noun.

So:

• svefnpoki = a sleeping bag
• svefnpokinn = the sleeping bag

Icelandic usually puts the at the end of the noun instead of using a separate word like English does.

It is a compound noun:

• svefn = sleep
• poki = bag

So svefnpoki literally means something like sleep-bag, i.e. sleeping bag.

Then svefnpokinn is the sleeping bag.

Hlýrri means warmer. It is the comparative form of hlýr (warm).

So:

• hlýr = warm
• hlýrri = warmer

After a comparative, Icelandic uses en for than:

• hlýrri en minn = warmer than mine

Because Icelandic can leave out the noun when it is already understood.

So minn here means:

• my one
• or more naturally in English, mine

The full idea is:

• hlýrri en minn [svefnpoki]

But the noun is omitted because it would be repetitive.

Because it matches the omitted noun svefnpokinn, which is masculine singular.

So minn agrees with the understood noun:

• minn = mine / my one referring to svefnpoki

If the hidden noun were feminine or neuter, the form would be different.

Here svo means so or therefore.

It links the first idea to the result:

• Her sleeping bag is warmer than mine,
• so she won’t get cold tonight.

So in this sentence svo expresses consequence.

Because Icelandic usually expresses feeling cold with an impersonal construction:

• henni verður kalt = she will get cold
• literally something like to her becomes cold

This is the normal Icelandic way to talk about someone feeling cold.

By contrast:

• hún verður köld

would more likely mean she becomes cold in a more literal or descriptive sense, not the everyday she feels cold / gets cold meaning.

Henni is the dative form of hún.

The construction e-m verður kalt requires the person experiencing the feeling to be in the dative case:

• mér verður kalt = I will get cold
• þér verður kalt = you will get cold
• henni verður kalt = she will get cold

So henni is there because the grammar of this expression requires dative.

Because in expressions like henni verður kalt, the adjective is normally in neuter singular:

• kalt = cold

It does not agree with the person’s gender here. This is part of the fixed Icelandic pattern for temperature and similar physical states:

• mér er kalt = I am cold
• honum er heitt = he is hot
• henni verður kalt = she will get cold

In a main clause, ekki usually comes after the finite verb.

So:

• henni verður ekki kalt

is the normal order.

A useful basic pattern is:

• verb + ekki

for simple negative main clauses.

Í nótt means tonight or during the night.

It is a fixed time expression, and Icelandic normally does not use the definite article here. So:

• í nótt = tonight
• not usually í nóttinni in this kind of meaning

This is just the standard idiomatic way to say it.