Here's a shelter idea:

Several years ago, I "found" an abandoned cat that I couldn't bring in, either. I created a shelter from the cat carrier. I put it on my patio, placed lots of towels inside, and an old rubber-backed throw rug over the top. Oh, I wrapped cardboard in a plastic garbage sack and placed it under the carrier to help prevent the cold coming up from the patio.

I put a bowl of food in it and immediately she knew it was for her! She went right in and lived there, protected from the snow, until I found her a home. (Except when it got too cold, I moved everything into the garage with a space heater.)

I had to rig the carrier door so it would stay open.

Good thoughts and prayers for this sweet kitty that deserves a loving home. Thank you for taking care of her.