what would have happened if I hadn't worn a hat?

I presume it’s still the case the US military has the outdoor hat fetish. Whether you were enlisted or an officer, you could get into trouble not wearing your hat outdoors.

Cockneys would have yelled at you in unfathomable slang:

“Don’ walk about wiffout yer cady on,
Ginger, you’re barmy!
Get yer hair cut, they’d all begin t’ cry
Wiff nuffin on yer ‘ead y’know you are a pie!
Pies must ‘ave a little bit of crust–
Why don’ you wear a cady?
If you wanna be a don you want a bit o’ somethin’ on
To take off to a lady!”

Hats outdoors are part of the uniform. If you don’t wear one you are out of uniform, a no no. Hats indoors are not worn unless you are armed.

I wear a fedora in the winter, - it keeps the rain and snow off my eyeglasses and does keep me warm. The only problem I have is finding a good ski hat - my 7 and 7/8 hat size makes a lot of hats too tight or impossible to keep on. One of my friends at work would sometimes borrow my fedora when she went outside to have a smoke. She got so many compliments while wearing it that she went out and bought her own.

When my old boss first went to work at AT&T in the early sixties, he was told to always have a hat - he did not have to wear it to a customer, but he should keep it in the office in case one of the higher ups walked by. I think part of the reason is that in the WWII military, a lot of people were taught the value of uniformity - group identity, cooperation and fitting in - and were made uncomfortable by those who didn’t. IMHO the children of the WWII generation stopped wearing hats for the sake of distinguishing themselves from their parents.

If you want a warm knit hat to fit your big head size, shop in the women’s department. Women’s hats are big, to allow for hairdos. If you get there early in the season, you can find one that’s not girly-looking. I wear a 7 and 7/8, myself, in some styles

I like to wear an Australian bushman’s hat (like a cowboy hat but more sensible). Actually, it’s just a plain, broad brimmed felt hat. It suits me. In fact, it suits damn near all men (and the ladies like it :D)
I currently don’t own one though, which is silly of me, just like it’s silly of the 99% of Australians who go about hatless in a t-shirt and short pants, and they wonder why we have the world’s highest incidence of skin cancer.

At my company, I saw a man sent home once - a grown man, professional engineer - because he forgot his tie. His home was an hour and a half round-trip away, and he was told that he was expected to make this time up after hours. So the men there kept a spare tie in their desk drawers, just in case. But it gets better than that - the tie had to “match”, because later on someone was told their tie was “too wrong” for their suit, and they would have been sent home except another man there had an “emergency tie” which they loaned the first man, which was a better fit.

And this was the mid-1990’s. Yeesh. But on-topic, I asked an older engineer there what would have happened if a man had forgotten his hat back then, and was told he would have been sent home, with a reprimand on his permanent record. Most men did keep an “emergency hat” to avoid that situation.