I used to be anti Baseball Cap
But, I started wearing a baseball cap under my hoods a few years back, and, being a specs wearer, found it transformed my wet weather hillwalking experience. Way better than the 'mountain caps' I'd worn previously
The 'you should get windsreen wipers for those' "jokes" have almost completely ceased due to the added protection the cap gives me.
And, I find the Montane litespeed hood unwearable without a cap -
My usual winter headwear now is baseball cap supplemented with a buff - if it's any colder, then I'll be wearing warm hood as well
My main issue with baseball caps is that most of them seem to be quite shallow at the rear and unless you have very short hair, won't stay on so well. I dread the day when I lose/destroy my current one.