It depends on both weather and date for me. For example, on a cool day in August, I would certainly wear something warmer, but it would be something that still said summer like a long sleeved cotton lawn shirt, or a light cardigan. For me, things like boots, corduroy, "real" sweaters, leather jackets, etc. wait until September 1st. Yes, it is arbitrary, and I know many people wear the things I've listed at any time, but those are "fall" items for me and I cannot get past the mental block that says I cannot wear them in June, July and August. Similarly, I will not wear a summer maxi dress after August.
This is mostly because I live in a 4 season climate, though, so I know that the "rules" are different for more temperate areas. Going on a cruise, for example, makes all the rules go out the window because we would be in a warm place in a different part of the world.