Nights were chilly in the late spring when we were in the CT, and it depends on what sort of restaurant you go to. We'd spent the days on the trails so we went to dinner at casual places in jeans and clean, tidy shirts and didn't feel out of place at all. There were a lot of other hikers around as dressed-down, or more, as we were. The fancier the place, the more you might want to adjust the wardrobe but it's a different animal than Venice.
Honestly, I didn't notice a 'dress code' much of anywhere we've been in Italy, and that includes Milan. Sure, a 5-star restaurant is going to demand a different sort of attire than a pizzeria, and a sightseer is going to have different demands on their feet and clothing than someone going to the office. It's all about what's normal and comfortable for you, and the locals really do not care. If you don't wear dresses at home (that would be me), don't wear them abroad. If you often do, then pack them.