<human>: I have a cat that sort of "adopted" me last spring. At first he would only sit at the edge of the yard, but after several weeks of gradually getting closer, he has become an incredibly affectionate cat. We have taken him to the vet and had all his shots and had him neutered. He comes inside whenever he wants, but he never stays long. He is usually ready to go back out in a few minutes. We made him an insulated house right outside our door for this winter, and he uses it regularly. But over the past few days, even his little house isn't warm enough for the harsh wind and snow we've been getting. He is more than willing to stay inside now, and has been happily lounging, sleeping, and eating to his heart' content for the last two days. 
I've been having trouble with him using his litter box, which is understandable because he's over a year old and has never used one before. I don't have the heart to put him out in the cold just to avoid cleaning after him. Is isolating him to our laundry room with this litter box (and bedding & food, but not right next to the litter box) enough to teach him to use it? I show it to him frequently and place him in it every time he finishes eating or appears to be looking for a place to go. 
The other  issue is that he freaks out in the room by himself. He's been meowing loudly for over 30 minutes. I feel like I'm abusing him, even though I'm just trying to make sure he doesn't freeze to death.  He has everything he needs in there, and has been content all day in the house; this only started when I isolated him to this room tonight so he can maybe figure out the litter box, or at least all his messes will be in one place and not scattered throughout my house. (Also, I've been careful to use the correct cleaners so that he doesn't try to use the same spots in the house again.)
Any tips, advice, or encouragement are welcome! Thank you in advance!

Condense the text into a few key points
<bot>: help me help my outdoor adult cat not freeze to death but also not shit all over my house and tear down my laundry room curtains.