What are signs my cat is in actual distress?

(I’m in Upstate NY USA)

New cat momma testing my outdoor stray on a life inside. He’ll happily hangout with me inside for a while but when he’s ready to leave he’ll start to cry by the door. If I ignore him, he’ll walk over to me and start nipping at me furiously so I just give up and let him out.

It’s going to be freezing soon and I want to try an overnight but how do I tell when he’s just annoyed about not being let out vs actually feeling trapped or in distress? It IS unusual for him to nip so I took that as a sign but I’m very very very new to cats and could use any advice. TY!