Have you read Elizabeth David’s book about the use of ice and ices across the ages? It was published back in the early 1980’s and is actually quite a scholarly affair with plenty of citations and references.
Chapter one discusses the use of snow and ice in early and medieval Florence and Venice. It talks about the problems of getting the snow down from the mountains and building snow caves and other structures to keep it all cool through into the hot summer days. There is also a little about the views of the medical profession back then as to whether or not chilled fruit and other combinations are good for you.