They do, and they always have. Here’s an interesting way to illustrate that: make reconstructions of modern animals as if we had no idea about the expected distribution of fat and other soft tissues. Here’s a baboon drawn from its bones while pretending ignorance of hair and lips and such unfossilized stuff:
This is from a book by John Conway, CM Kosemen, and Darren Naish, called All Yesterdays: Unique and Speculative Views of Dinosaurs and Other Prehistoric Animals. I’m going to have to add it to my list.