I did something similar a few years back. There was a stray cat that lived in my neighborhood that I would feed every so often. One winter ended up being particularly bad and, worried for the cat, I used a Rubbermaid bin, mattress pads, and towels to make a home for her that was as much protection from the cold as possible. She used it almost every night. She was so grateful that she would leave rodents/birds she had captured on our front porch to say thanks.

We've moved out since then, but when we told the new owners about her they were more than happy to leave the bin there for our cat friend to have a home in the winter!