Learn Russian: Например, в этих городах холодно зимой. - For example, it is cold in these cities in winter.

This phrase means 'in these cities'. Because it describes a location after the preposition в (in), it must be in the Prepositional case. Since we are talking about multiple cities, we use the plural Prepositional endings: -их for the plural demonstrative pronoun этих (these) and -ах for the plural hard noun городах (cities).

The singular word for city is город. How exactly do we form the plural городах?

Город has an irregular plural. Its Nominative plural form is города (cities) instead of using a regular ending. The Prepositional plural case usually adds -ах or -ях to the plural stem of a word. Since the irregular plural stem already gives us города-, we simply add -х to get городах.

How does холодно translate to 'it is cold' without words for 'it' or 'is'?

When describing weather, the environment, or how someone feels, Russian uses an impersonal structure. There is no subject ('it') and no present-tense verb ('is'). You simply use the adverb form ending in -о, like холодно (cold), жарко (hot), or тепло (warm).

Why is the word for winter written as зимой here instead of зима?