I've never found a covered litter box did anything to discourage a dog from raiding cat poop. You can get all sorts of boxes though that will make it hard for dogs to get in but they tend to be expensive! The easiest approach is to have litter boxes in places the cats can access but dogs cannot.
Most cats incidentally, dislike using covered litter boxes -- same reason we tend to dislike portable outdoor toilets. Small enclosed space where you have to smell everything that has been done inside that small space. Ugh. Many cats will tolerate a covered a box. But it is a lot nicer for cats to not have to use them. And often the main reason cats stop using a litter box is because they finally have had enough of a covered box.
Hooded or covered litter boxes are popular with consumers, but if cats did the shopping, they would be left on the shelves. Humans do not want to see or smell what kitty leaves behind in the litter box, but for that matter, neither does kitty. The hooded litter box forces him to enter a cramped, cave-like structure that concentrates odors, creating an outhouse effect. Since the cat's sense of smell is at least 14 times more sensitive than ours, this may be all it takes to send kitty in search of a fresher smelling toilet area...