Heh, yeah, they scamper everywhere. And I think he buries most of them. I've never seen a squirrel so obsessed with burying nuts, he really goes to town. I think he'd come to the door every 10 minutes all day long, but I don't want our yard or the neighbors yards being nothing but peanuts so I only give him a handful.
Mine are indoor-only, but there's about 6 cats who periodically frequent our yard. The squirrels don't seem very bothered by them. They'll even be aggressive and chase/battle the cats when they get too close, which is funny. But most of the cats here aren't very big - just the 5-7 lb sort.
Out door pets. I have fox squirrels around my place, I feed them bird seed.