Back in June I fed a young stray cat that was on my patio. It's been hanging around ever since. I would guess it's 8-12 months old.

Now that it's been getting colder it will sleep in the house but doesn't want to stay indoors for long.

This is the first winter cold night (20 degrees F) and I was not going to let the cat out, but it kept yowling for hours and I finally said F it since there's a semi-heated cat house near the back door it can retreat to. It still makes me worried something might happen though.

If anyone has an indoor/outdoor cat, what do you do when it gets this cold and the cat desperately wants outside?

Weird. Cats dislike the cold.

We adopted a blind baby cat from street, She is a curious sort but avoids danger

If something happens (injury w/e), cats often have the habit to hide and not necessarily to go straight back home. So in that case, if it's cold the cat freezes to death. It happens a lot. If the cat just stays close by, it shouldn't be a problem. Temperature tolerance also depends on the type of cat, 20 degrees might be okay for a Norwegian forest cat, but not every cat can handle that. The cat itself doesn't know that, so it's up to the owner to be responsible.

Might have to go to the bathroom. I have several litter boxes but they still like to go out. One loves cold weather, her sister is a little heavier and out of shape and doesn't like outdoors much. But after a month or two of it being cold the second one adapts also. Then she purrs like crazy when she's outside and its 30F. Makes no sense to me.

When it gets too cold out.. too fking bad cat, you're not going outside. (He or she will be fine)

I have a Norwegian forest cat so I let it out lmao

You let him out. Try to insulate the cat house with some straw, or something else that wont really hold onto moisture, and give him easy access to food. Be sure not to leave so much out that it attracts other animals. We had a group of ferals around our house and we added straw to a waterproof box, with two holes. One for entry and one for easy escape if need be. We'd open the box and just find them huddled together. It was pretty damn cute. Let the little brah go outside and earn his keep by killing all the vermin in the area looking to keep warm during the winter.