Keeping your face warm in the rain?

A good hat with a wide stiff brim might be all that you need. Keeping your face dry may do more than a lot of extra insulation.

if it is not windy: try an umbrella

otherwise wear a good rain jacket with a good hood and a good and high collar.
you can also wear a baseball cap to keep the rain of your face and just put a synthetic buff over your nose.

What about a neoprene face mask (aka half mask)? They are commonly sold for motorcyclists and snowmobilers…it's not a balaclava, just a wrap-around face mask. It would do a good job keeping your face warm without restricting heat loss from your head and neck the way a balaclava would.

My wife and I fight over the Smartwool neck gaiter.

For actual protection and gangsta points I use my Ninjaclava (with the two little stitches cut *thx Bryce*)

But for chilly hiking the SW neck gaiter is pretty nice to breathe through. When it gets too wet, spin it a half turn.

I find my wide brimmed hat is usually all I need even in bad downpours. Sometimes I'll pull the rain hood up over it to give extra protection. Also an umbrella as has already been mentioned can be invaluable. Even in moderate winds I can angle it to keep rain off my head. I've never found any kind of wet insulation on my face to be much help. Keeping water off the face is the best approach.