Headsweats makes a great cycling cap: Cycle Cap | Retro Cycling Caps | White Cycling Cap - Headsweats

In warm weather, including rain, it's all I wear. You can adjust how low the brim is by adjusting the position of the cap on your head. I have no issues seeing around the brim even in my most aero position.

I always wear glasses on the bike. A droplet of rain (or worse, hail) in the eye at 30+ mph is not cool. I use my finger as a wiper to occasionally clear the lenses. I wear contacts FWIW.

How about a helmet with built in visor so you can wear your glasses under the shield. At least you can wipe the shield as needed without touching your glasses.

Personally, I'd fog that shield up so quick I probably wouldn't make it out of my neighborhood without losing all vision. In the rain I have frequently had to pull my glasses down at traffic lights and keep them down until I get moving again when the wind will resume clearing the fog created by my warmth. I also use my glasses as a mount for my rear view mirror so anything that prevents that setup from working is a no-go.

Hat with brim? Check
Glasses? Check
Mirror? Check
Helmet? Whut? :p

I had a little sprinkle on my ride in today, the cap didn't save my glasses but it helped VS. no cap.

It helps for sure
 

I always ride with a cap, rain or shine. I rode in a light rain yesterday and the cap definitely reduces the amount of rain on my lenses. I use the Voler Caliber cap, perfect material (thin) and the best bill I've found (big enough to make a difference but doesn't hinder line of sight). This cap also is easy to reposition while riding if I need more eye coverage.

I ride mostly solo (especially if roads are wet) so spray from a rider in front isn't an issue.

I always wear a helmet, always wear a cap, and always wear prescription glasses. The cap doesn't stop ALL rain, but it helps. I've tried riding in the rain without glasses, but found that I was squinting so much and catching enough road debris that I was better off looking through wet, smeary glasses.
The worst is racing in the rain - because you're constantly getting spray from the rider's wheel in front of you. You're essentially forces to choose between betting a steady spray of dirty water to the fact or being out in the wind.
Crux of the matter - riding in the rain sucks, but rain is part of the road.