One should remember that the global domination of bottom fermented beers like lagers, which requires long periods of cold fermentation, are historically a relatively new thing.

Ancient beer would mainly be top fermented ales which does not necessarily require temperatures below room temperature in order to properly ferment.

Anyway, when bottom fermented beers like lagers began to gain popularity in the Western world in the 19th century, breweries usually used underground storage facilites, like bunkers, and placed blocks of ice to further cool the temperature.

Source: Martyn Cornell, Beer - The Story of the Pint, Headline, 2004.