I usually just pick off the crud-all my girlies are fans of cleaning–but if I’m bathing, CONDITIONER works great to get it all off. Just slather on in the beginning of the bath and then wipe off at the end, maybe with one quick rinse from the hose, or with a sponge, and done. The conditioner doesn’t strip any oils and really does a good job of cutting through all that greasy stuff!
Generic KY Jelly. Works great and you don’t have to worry if some is left on like shampoos, Vaseline (which attracts dirt), etc. I usually do a quick check with gloves and as long as I stay on top of it, nothing accumulates.
I just use my fingers as part of regular grooming. If it’s really crusty, I use a baby wipe or a warm washcloth.
I have one mare that is fine with it and another who is not very thrilled with me being in her personal space like that–I want something that is quick and easy for her. 
We’ve never had a mare that didn’t absolutely love their nether regions cleaned. It’s the itchiest spot ever!
We would just use plain water and a washcloth, and then when clean, put on some udder balm (the aloe cattle kind is cheaper than the equine kind and has the same ingredients ).
I avoid anything greasy as it attracts dust etc. I use baby wipes, with lotion added and clean gently. Can’t say mare gets ecstatic but certainly never objects.
Same here. I use my hand and a damp cloth. Sometimes they raise up the hind leg so I can reach easily, or they park out and spread their hind legs a bit. It’s cute.
I don’t use lotion or any balms because it is dusty and I don’t want their skin to be sticky and attract dirt, and I haven’t noticed dry skin problems.
