Buy it a plastic igloo cat shelter. If it uses it then put it away in the spring. If it doesn’t then donate it to an animal shelter. This is kind of strange. Cats are different.
Best shelter is a large plastic storage bin with lid tied on and a hole cut in the top at one end then the thing laid on its side. I have the porch furniture cushions in the one I made for the two porch cats that have adopted me.