Walking in the rain with no makeup is totally fine -- I love it! But it's when a gal has gone to the trouble to put all the expected makeup and mascara on and maybe even temporary hair dye that it runs and makes a scary mess! Way worse that the original bare face.
If a gal has make up on, she needs to be sure she has a hat or an umbrella with her and a handkerchief! I get stuck in the rain from time to time, with my weddings, full makeup on for everyone - I always carry enough umbrellas for everyone, but once in a while I'm the one who has to stand without the umbrella and so I get the drips over my makeup - luckily it's not necessary that I'm in front of the camera!
That's where performing my weddings in a full face snorkel mask or face shield would come in handy!