Maybe I can give a little insight on the whole bathing a cat thing.
Obviously, cats don't like the water, unless they're drinking it. At pet shops, like Petco, they have different things in order to wash them without water. Bath wipes, waterless shampoo. Some cats don't mind getting a bath but others will scratch you to death before putting them into a tub. I'm not too sure if the whole holding them by the nape of their neck really works. I know when you go to a vet and you need to hold them, they tell you to hold them there to keep them still. If anything, just use the quick stuff. They work just as well and probably alot easier.
When it comes to dogs and baths, they don't mind it BUT... don't do it all that often. Unlike us, we can lotion and moisterize and get our skin the way we want if it's dry. Dogs don't have that option. The more you wash a dog, the more you dry up their skin. Plus, in the winter time, they're more prone to getting sick if they're wet and it's cold outside.
Hope that helps everyone.