Rain visor?

Simple foam visor.  Doesn’t absorb water.  Something like https://www.amazon.com/dp/B09JTTQC8H

sometimes I have a hat with wide brim under hood which helps

Since I make my own raincoat, I make a wide stiff brim

I just wear the same ball cap I wear when it isn’t raining :)  Also keeps the plastic hood fabric off my head.

Ball cap for the win.  And as JCH alludes, it’s probably more important for keeping the rain hood from covering your eyes than anything else.

For light or short-lived rain, my regular hat does fine by itself, but if heavy or sustained rain is in the forecast, I leave the Tilley at home and take the ball cap.

I use a ball cap, although it is mostly to keep the rain drops off my glasses.  I have a big straw hat I use during the summer (without using the hood).  There is also the umbrella.

I forgot to say that I typically don’t have a hood deployed because I want ventilation to keep me from overheating.  My hat keeps my head and neck dry: the odd but functional Montbell Rain Umbrero. which is painted on the inside to also provide sun protection.

Foam visor, from the kit I received  for the 2000 Portland  Marathon. I’ve  found it so useful,  I bought some sheet foam, traced the design,  and made a few spares, in case I should  lose the  original.  Also works with a windshirt hood, when it’s sunny and hot but too windy for my sunbrella.

Kelly

I normally wear a wide brim hat, which will work under a hood since I’m often out from under tree cover. That said, I often carry a lighweight runners cap (essentially a baseball cap with a lot of mesh), like the OR Swift Cap, that I usually wear when it’s raining. It keeps the rain off my glasses and more of my face. If I’m hiking more in forested trail, then I may just take a ball cap and leave the wide brim hat at home.