Here's why:
* Possessive pronouns show ownership. Examples include: mine, yours, his, hers, its, ours, theirs.
* "Its" in this sentence is used as a possessive adjective, describing the paws. It's telling us which paws are caked in mud.
Think of it this way:
* Possessive pronoun: "The mud was all over *its* paws" (Here, "its" stands in for "the paws" and shows ownership).
* Possessive adjective: "Its paws were caked in the mud" (Here, "its" modifies the noun "paws" and describes them).