The Romans had "snow shops", and also stored snow in underground ice-houses until it turned to ice - Seneca remarks that rich Romans would pay more for ice from the bottom of the pit. Pliny the Younger refers to snow being used to with sweet wine (or rather not being used, as his friend did not turn up to a dinner party). Ice houses go back as far as 1700BC at Mari in NW Iraq, when Zimri-Lin had one built by the side of the Euphrates, but I'm not sure that was used for chilling drinks.
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