Sausages may be housed in animal intestines, but I'd be surprised if hotdogs were. I think hotdogs retain their shape just from the pre-cooking process they all go through before being packaged. Correct me if I'm wrong.
You are only about 1/3rd wrong (but mostly correct)! Hotdogs absolutely have casings, sometimes natural animal intestine of pork or sheep, other organs, and collagen casings --those are edible, and stay on the 'dogs. Others use things like cellulose, and various filler type ingredients to create a casing, and those are stripped off before shipping. If you don't know the ingredients, you can usually tell if it's natural casing from the extra stiffness in the bite. And they're usually more expensive, lol