My three mares all love when I get rid of their crud. One started off as a kicker if I touched anywhere on her belly or even thought about touching her udder, but once I persisted by getting closer and closer every day, she is now a convert and loves it as much as the other two. Two of the three ARE subject to Pony Club inspections, so there’s that, but they also seem very happy to get it cleaned out from time to time. I use my fingers and pick stuff out, and when they’re getting baths anyway, will do a full cleaning with shampoo and water. I think maintenance with baby wipes would probably be a good idea.
Something oil based to loosen up the crud (coconut oil, etc.). Slather it on (be generous) and then go for a ride! By the time you get done everything will be soft and easy to deal with.
I clean my mare every time we rinse off from a ride. She can get crud but she is fine with a rinse and scrub with your fingers. She has had a foal so she could care less. I would imagine for a maiden mare it would get easier with time and repetition!
My mare is a bit of a hussy and will walk along side of me in the pen and stop me at her flank so I can clean things up. She LOVES it. Even when she’s perfectly clean.