How is this act normally performed? Well, in the household where I grew up parent grabbed back of child's head, held firmly, took cold wet washcloth, and forced it into child's (my) face. Yeah - what's not to love about this? Oh, and accompanied by annoyed, loud statement like, "Now, JUST HOLD STILL!" Or "This will just take...stop! STOP IT!!". Or, if you're in Scotland or a Pink Floyd album, "STAND STILL, LADDIE!!!". :-)
OK, so, basically, from my vague 60-year-ago recollections of this, it sucks bigtime. Large person with loud mouth is now going to force a cold wet rag into my face, smear it all over, and get angry with me. I'm going to fight it because, well, that's what we DO as kids - we fight back! STAND UP TO THE MAN! EVEN IF HE'S A WOMAN!! DON'T LET THE MAN BRING YOU DOWN!!! YOU GOTTA FIGHT FOR YOUR RIGHT TO PAAAAAARRRTY!!!!
So, how to handle better? Well, #1 - cold and wet ain't cool. And #2 - being forced ain't cool neither. Toss a damp paper towel in the microwave for 10 seconds, make sure it's not burning hot, then hand it to child and ask them (ASK them!) to wipe their face. If they say "No!", and they will, smile and say "OK", pick up the towel, and walk away. From a kid's point of view, THIS IS EMPOWERMENT! YEAH!! I DONE STUCK IT TO THE MAN!!! OR THE WOMAN!!! WHATEVAH!!!! But...now my face is icky and sticky and...WOMAN?!? WHERE'S MY TOWEL??? I DEMAND YOU BRING MY TOWEL HERE, THIS INSTANT!!! And don't be givin' me no jive about "But I thought you didn't want it, dearest?"!!! I WAS JUST TESTIN' YOU!!!! WHERE IS MY TOWEL?!?!? I BETTER BE GETTIN' MY TOWEL HERE AND PRETTY DANG QUICK OR WE ARE GONNA BE HAVIN' US A LOADED DIAPER, MOMMA!!! UH-HUH!!!!!
Basically, you trick 'em. You offer, they refuse, you take away. Maybe toss in, "Say bye-bye to Mr. Towel" so they know the towel - THEIR towel! - is now going away. Fastest way to get 'em to want something is to give it, then remove it. Basic child-and-executive psychology. :-)