Yes! Men in the US stopped wearing hats regularly during the Kennedy administration.
Some things about women's clothing might surprise Steve as well - above all, the variations in what he might see women wearing at the same time and the same place. Think about the range of types of clothing people were wearing at the supermarket, the last time you were there. That kind of variation in acceptable attire for an activity was just not happening in 1945, I don't think; on the other hand, that made small differences - half an inch in skirt length, for instance, or small prints vs large prints - very meaningful, in a way that they're not so much now. Or at least I don't think they are now. I am way out of my field here, though!
Re: Hats!
Some things about women's clothing might surprise Steve as well - above all, the variations in what he might see women wearing at the same time and the same place. Think about the range of types of clothing people were wearing at the supermarket, the last time you were there. That kind of variation in acceptable attire for an activity was just not happening in 1945, I don't think; on the other hand, that made small differences - half an inch in skirt length, for instance, or small prints vs large prints - very meaningful, in a way that they're not so much now. Or at least I don't think they are now. I am way out of my field here, though!