Both os my cats will gnaw nepeta (cat mint) to the ground. That's ok by me because we have it growing wild all over the place and it can be quite invasive. When I pull it up, I toss it to the cat who will hold it to his face with both paws and just chomp.
Around here, the wild common type of nepeta is drought tolerant and winter hardy. I live in a semi arid plain that sometimes doesn't get rain for weeks or even months.