Italians like their drinks warmer than Americans like theirs. So, if you want ice you will have to ask for ice.
Several years ago I was eating dinner by myself in a small outdoor café on the Via Veneto in Rome. I entertained myself by watching the other diners. Since it was early to be eating dinner by Italian standards, most of the Italians were enjoying a drink and a snack.
I happened to be sitting next to a table of four elderly women and one elderly man. They were all dressed extremely well in their suits and hats. One of the women had a bright green drink that had been delivered to her full of ice. After much discussion with the waiter and much complaining to her friends she meticulously picked out each and every sliver of ice and put it on her plate.
Having lived most of my life in the US I have been brainwashed by the advertisements of Coca Cola being poured in a glass full of ice with the scorching sun burning in the background. I like my drinks cold.
When in Italy, if I want a Coca Cola with ice I say it in Italian, “vorrei una Coca Cola con ghiaccio.” If you are lucky you will get a glass full of ice and a bottle of Coke. Of course, it is also possible that they will decide you don’t know what you are talking about and bring you a glass without any ice or with only one cube.
On the other hand, in Italy, you will often be served red wine that is slightly chilled.
Part of the joy of travel is seeing the little cultural differences in different countries. Warm drinks or cold red wine won’t matter since they will be accompanied by some of the best food the world has to offer.