“I’m hungry! I’m cold! I’m hurt! Please let me in! I need attention!”. Of course, if you do open the door, the cat may promptly run away—but it will probably be back. If you keep offering to take it inside, I think sooner or later—when conditions outside get REALLY bad—it will take you up on your offer. Once inside, the cat may run and hide. In which case, set out food, water, and litter, and wait for it to emerge. This may take a while.