Learn Hardcore Norwegian: Til tross for den fuktige luften holder termosene drikken varm og soveposene tørre. - Despite the damp air, the thermoses keep the drink warm and the sleeping bags dry.

På tross av den fuktige luften – also natural, same meaning.
Selv om luften er fuktig – literally “Even though the air is humid”.
Here you must use a full clause (with a verb), not just a noun.

So:

Til/på tross for den fuktige luften, holder termosene …
Selv om luften er fuktig, holder termosene …

Same idea, different structure (prepositional phrase vs. subordinate clause).

Why does the word order start with Til tross for den fuktige luften holder… and not …termosene holder…?

Norwegian is a V2 language in main clauses: the finite verb (here holder) must usually be in second position, no matter what comes first.

Positions here:

Til tross for den fuktige luften – fronted adverbial phrase (position 1)
holder – finite verb (position 2, as required)
termosene – subject
drikken varm og soveposene tørre – objects and complements

If you don’t front anything, you get the more neutral order:

Termosene holder drikken varm og soveposene tørre.

Both are correct; the given sentence just emphasizes the “despite the humid air” part by putting it first.

Why do we say den fuktige luften with both den and -en on luften? Isn’t that “double” definiteness?

Yes, this is double definiteness, which is normal in Norwegian with:

a definite noun
plus an adjective
plus a determiner like den/det/de

Pattern:

den
- fuktige
  - luft
    - -en
      = den fuktige luften (the humid air)

You need both:

The article/demonstrative: den
The definite suffix: -en

Compare:

luft – (some) air
luften – the air
fuktig luft – humid air
den fuktige luften – the humid air

Without the adjective, you’d just say luften, not den luften (unless you want a special emphasis like “that air”).

Why is it fuktige and not fuktig in den fuktige luften?

Adjectives in Norwegian change form depending on definiteness and number.

General rules (Bokmål):

Indefinite singular common gender: fuktig luft
Indefinite singular neuter: fuktig / fuktigt (often just fuktig in modern Bokmål)
Indefinite plural: fuktige rom
Definite singular with den/det
- noun: den fuktige luften
Definite plural with de
- noun: de fuktige rommene

In den fuktige luften, the noun is definite and has den before it, so the adjective takes the -e form: fuktige.

What are the genders and forms of luften, termosene, soveposene, and drikken?

All of them here are definite forms:

luft (en) – air
- indefinite: en luft
- definite: luften / lufta
termos (en) – thermos (flask)
- indefinite singular: en termos
- definite singular: termosen
- indefinite plural: termoser
- definite plural: termosene (the thermoses)
sovepose (en) – sleeping bag
- indefinite singular: en sovepose
- definite singular: soveposen
- indefinite plural: soveposer
- definite plural: soveposene (the sleeping bags)
drikke (en) (noun) – a drink / beverage
- indefinite: en drikke
- definite: drikken (the drink)

All are common gender (en-words) in this sentence.

Why is it drikken varm but soveposene tørre? Why not drikken varme as well?

Varm and tørre are predicative adjectives describing the objects:

holder drikken varm – keeps the drink warm
holder soveposene tørre – keeps the sleeping bags dry

They must agree with the number of the noun they describe:

drikken – singular → varm (singular form)
soveposene – plural → tørre (plural form of tørr)

For tørr:

base form: tørr
plural/definite form: tørre

Also, predicative adjectives usually use the indefinite form, even when the noun is definite:

Drikken er varm. (not drikken er varme)
Soveposene er tørre.

So:

singular: drikken varm
plural: soveposene tørre

Could the sentence also be Termosene holder drikken varm og soveposene tørre til tross for den fuktige luften?

Yes, that is grammatically correct:

Termosene holder drikken varm og soveposene tørre til tross for den fuktige luften.

Now the clause starts with the subject (Termosene) and ends with the concessive phrase (til tross for den fuktige luften).

Meaning and grammar stay the same; only the information structure / emphasis changes slightly:

Original: emphasizes the “despite the humid air” part by putting it first.
Reordered: starts with what the thermoses do, then adds the despite phrase at the end.

Is drikken related to the verb å drikke (to drink)?

Yes. Norwegian often uses the same stem for verbs and related nouns:

å drikke – to drink
en drikke – a drink / beverage
drikken – the drink

In this sentence, drikken is clearly a noun (the drink or the beverage inside the thermos), not a verb form.

Why is the verb holde used here? How does holde noe varmt/tørt work?

Å holde is used in Norwegian much like English “to keep” in this pattern:

holde noe varmt – keep something warm
holde noe tørt – keep something dry
holde noe rent – keep something clean

Structure:

Subjekt + holder + objekt + adjektiv
- Termosene holder drikken varm.
- Soveposene holder deg varm.

We don’t use beholde (to retain, to keep for yourself) here, because the meaning is not “keep possession of” but “keep in a certain state/condition”.

Can I say Selv om luften er fuktig, holder termosene drikken varm og soveposene tørre instead? Is that natural?

Yes, that’s perfectly natural:

Selv om luften er fuktig, holder termosene drikken varm og soveposene tørre.

Differences:

Til tross for den fuktige luften – prepositional phrase with a noun.
Selv om luften er fuktig – subordinate clause with a verb (er).

Both express concession (“even though / despite”). Choice is mostly stylistic and about whether you want a noun phrase or a full clause there.

Could the sentence be Til tross for den fuktige luften holder termosene drikken og soveposene tørre (one adjective only at the end)?

Yes, but the meaning shifts slightly.

Til tross for den fuktige luften holder termosene drikken varm og soveposene tørre.
→ The drink is warm, the sleeping bags are dry (two different states).
Til tross for den fuktige luften holder termosene drikken og soveposene tørre.
→ Both the drink and the sleeping bags are dry (which is odd: a “dry drink” doesn’t really make sense).

Using varm only once like this is fine:

… holder drikken og soveposene varme.
→ Both are warm.

So grammatically you can share one adjective at the end, but it must logically fit both nouns.

Are varm and tørre adjectives or adverbs here?

They are adjectives, used as predicative complements of the objects:

drikken varm – the drink (is) warm
soveposene tørre – the sleeping bags (are) dry

The verb holde here has the pattern:

holde + objekt + predikativt adjektiv
(keep + object + adjective describing its state)

Norwegian usually uses a neuter -t form for true adverbs (from adjectives), e.g.:

snakk høyt – speak loudly
løp fort – run fast

Since varm and tørre describe nouns, not the verb, they are adjectives, not adverbs.