In the 1820s Frederick Tudor started his business harvesting ice from New England ponds and sold them packed with sawdust to the South, the Carribean, and Europe. Eventually it became a global business empire that shipped ice all the way to India.
Theoritically this industry was possible anywhere that has ice in the winters and decent ships. So what impact would it have if the ice industry existed in earlier times - say Roman Empire, Middle Ages, Song dynasty, etc? Ice wasn't just useful for making ice cream and frozen drinks of course, the ice box was an early form of refrigeration which kept food fresh for days instead of hours.