I'd like to keep them out, but when I close the door both of my big old slob cats raise a ruckus. They howl and claw at the door and make a general nuisance of themselves. In fact they can't stand ANY door in the house to be closed if there is one of their humans inside of it.
My dog comes in, lays down looking out of the long window, and sighs deeply every once in a while. I think he believes he has to be there for my sake, but he'd really rather be someplace else. But he won't stay out. As soon as I move my chair back as though I'm going to leave the room, every one of them makes a mad rush to the door to be the first one out.
Animals can be very strange. 8-)