The Snow Cat is a godly figure worshipped by Snow Leopards instead of the Great Dragon. The Snow Cat is not its own distinct being, and is actually how the Snow Leopards interpret The Great Dragon.
When Snow Leopards hunt or eat their prey, they typically say things along the lines of "Thank you, Snow Cat, for this prey". Phrases have also been said in the series like "Thank the Snow Cat!" numerous times, by Leopards.