| This answer is opinion-based.|
Due to lack of canonical information in the franchise, there is no definite answer to this question.
Animals in general have more natural protection against the elements than brittle, bare-skin humans do, hence why we require more intricate clothing, shelter, and other common necessities just to survive. In the case of anthropomorphic animals, they typically tend to (at the discretion of their universe creators) reflect some of their real-world animal counterparts' characteristics.
In the Kung Fu Panda universe, most of the characters have fur or feather coatings, and as such don't require extra cover or comfort for sleeping, much like their real-world counterparts. It appears to be the same case with other animals like snakes, rhinos, and pigs, who also reflect their animal counterparts despite not having as much natural protection.