You’ve had great responses here already. IMO, it really depends, each horse is an individual. My geldings get inspected when they exhibit themselves, as opportunity presents itself, which is fairly often, while I am cleaning paddocks. We know each other well, I’ve raised them all from babies. Any major “rust” (smegma) gets picked off as necessary. I check for a bean. Haven’t found one in years now, but when I do, it pops out pretty easy. Depends on the horse, whether or not they get a bean. If you want to wash it, warm water (or KY) ONLY. Nothing else. Any skin irritation from products used will only elicit the production of more build up due to the irritation and skin inflammation, make it necessary to wash MORE often. It does not need to be “squeaky” clean, in fact, it’s better for the skin if it’s not. The naturally occurring skin bacteria is what keeps the skin healthy. Don’t remove it. As long as your gelding doesn’t mind, you can remove any major smegma bits (the “rust” I was referring to earlier), and check quickly for a bean whenever the opportunity presents itself in your presence. Just let him know in advance of your goals, introduce yourself first.
If you rely on your vet to do this for you, “surprise!!!”, it will be washed, and you will be billed for this. It may not need washing, and there may or may not be a bean, but it will be washed anyway. By all means, when you have not dealt with this before, ask for input and information from your vet. If your horse is shy about this, when tranquilization for dentistry is done is the best time to at least take a look, and see what, if anything, needs to be done. Check for growths or tumours or skin infections.