A male horse needs to have his sheath and penis cleaned periodically. It is an unsavory, but necessary task. Most breeding stallions are probably washed often enough during breeding season, but they might not get proper attention during the rest of the year. Stallions who are pasture-bred could easily get ignored, but geldings are the ones who most often have problems. An accumulation of dirt and excretions called smegma builds up in the area, and must be removed.
Mares experience the same affliction between their udders.
One of the first signs you may see, if your horse has dirty genitals, is tail rubbing. There can be several reasons for tail rubbing, but if you worm regularly, and are not plagued by parasites such as lice, a dirty udder or sheath should be high on your list of suspects. There is no exact answer to that question. It varies from horse to horse, and each area of the country is probably different. In Arizona and neighboring parts of the Southwest, horses seem to get filthy quickly.