It got colder as the night wore on.

Literal

Night [subj-が] deepen-[as-につれて] became-cold.

~につれて ('as X, in proportion to X') is a gradual-change pattern, attached to dictionary-form verbs or nouns. Expresses parallel change over time: as one thing increases/progresses, another changes alongside. 寒くなる ('become cold') is the adjective-becomes-state pattern.