A few years ago I visited the
beer museum in Bamberg, which is built down into a large hill. One of the rooms was indeed where they kept ice. (I tried to find
online pictures but there's not much to see, just a big room with stone walls.)
This is also how Biergartens came about, from
Wikipedia:
Numerous conflagrations had occurred, which resulted in the prohibition of brewing during the summer months. In response, large breweries dug cellars in the banks of the River Isar to keep their beer cool during storage. "Beer cellars" for consuming beer on premises naturally followed.
To further reduce the cellar temperature during the warm seasons, 19th-century brewers layered gravel upon the cellars by the bluffs and planted horse-chestnut trees for their dense spreading canopies and shallow roots, which would not damage the cellars.[4] Soon afterward, serving cool beer in a pleasant shaded setting emerged. Simple tables and benches were set up among the trees, creating the popular "beer garden" that is known today.