Learn Hardcore French: Nous offrons de l'eau froide aux invités.

French uses the partitive article to express some of an uncountable noun. Here, eau (water) is feminine singular and begins with a vowel, so de + la contracts to de l’.

l’eau froide = “the cold water” (specific water)
une eau froide = “a cold water” (rare, since water is uncountable here)
de l’eau froide = “some cold water” (unspecified quantity)

Why does the adjective froid become froide, and why is it placed after the noun eau?

Agreement: In French, adjectives must agree in gender and number with the noun they modify. Eau is feminine singular, so froid takes an extra -e → froide.
Word order: Most French adjectives (including froid) come after the noun. Only certain short or very common adjectives (BAGS: Beauty, Age, Goodness, Size) often precede the noun.

Why do we say aux invités instead of à les invités or just les invités?

offrir (to offer) requires a direct object (the thing offered) and an indirect object (the recipient), introduced by à.
à + les contracts to aux before a plural noun.
So aux invités means “to the guests.” Omitting à would make les invités the direct object, which doesn’t match offrir’s grammar.

How is offrir conjugated in nous offrons, and why is it spelled with a double f?

Offrir is a third-group -ir verb but takes the same present-tense endings as regular -er verbs:
je offre, tu offres, il/elle offre, nous offrons, vous offrez, ils/elles offrent.
The double ff is a spelling convention to keep the vowel o pronounced /ɔ/ (as in “law”) in every form.

Why is the subject pronoun nous necessary here? Could you use on instead?

French requires an explicit subject pronoun before the verb (except in some informal imperatives).
Nous clearly marks “we.”
In spoken, colloquial French, on often replaces nous to mean “we,” so you can say:
“On offre de l’eau froide aux invités.”
But nous is more formal or typical in writing.

What tense is offrons, and what nuance does it convey?

Offrons is the présent de l’indicatif. It describes an action happening now or a habitual/general action:

“We offer (we are offering) some cold water to the guests.”

How do you pronounce Nous offrons de l’eau froide aux invités?

A simple phonetic guide:
noo zoh-FROHN duh lo frwahd oh zahn-vee-TAY
Notes:

eau = /o/ (like “go”)
oi in froide = /wa/
There is a liaison between nous and offrons: /nu zɔfʁɔ̃/