"Tree cats" - I like that! I call my cats "Couch Panthers".
The big fluffy one likes to sprawl in the middle of the floor on his back, so when he's doing that his nickname is "Carpet Otter".
I have a baby gate to keep the critters out of my sewing/living room. The younger cat could hop right over it if he wanted to, but he doesn't seem to realize that.
It's a nice bonus for when we have a delivery; we have 3 dogs and they like to rush the front door and make all sorts of racket when someone's on the porch. But now the baby gate holds them back so we can receive a package or a pizza without quite as much chaos.
The baby gate doesn't do much to keep back the airborne fuzz though. Two long-haired cats and three mostly-indoor dogs...it's inevitable that some fuzz makes its way in.