Learn Icelandic: Það er alltaf kalt í stórum galleríum.

This is the dative plural ending! The preposition í takes the dative case when describing a stationary location (like being inside the galleries). Since galleríum is a dative plural noun, the strong adjective stór (big) must match it, becoming stórum. In the dative plural, strong adjectives and nouns conveniently share this exact same -um ending.

Why is the word for cold kalt instead of the dictionary form kaldur?

In Icelandic, adjectives must agree with the noun or pronoun they describe. Here, kalt is not describing the galleries; it is describing the general situation or weather represented by the dummy subject Það (It). Because Það is a neuter pronoun, the adjective takes the neuter singular form kalt.

Why does the preposition í take the dative case here instead of the accusative?

The preposition í triggers the dative case when it describes a fixed location, meaning something is just sitting or happening in a place without moving to a new one. If the sentence were about moving into the galleries from the outside, í would trigger the accusative case instead.

Is gallerí a loanword, and does it follow normal Icelandic rules?