We have three outdoor barn cats who have decided to take up residence in different areas of the property. One cat mainly lives in the barn, one mainly lives in the garage, and the third mainly lives on and under the porch. During the winter - they are all quite cozy where they decide to sleep. We've set up boxes with blankets, but they will get cozy wherever there's fluffy things like straw.
If you Google cold weather feral cat shelters - you can learn how to make them more cold-weather proof. I'd consider making a cat house this year just because the fellow who is now living on the porch hasn't lived a winter with us yet.
None of the cats have been indoor cats and are all neutered/vaccinated and treated monthly with Revolution.
Good luck! And good luck getting out the odors. Have you tried Nature's Miracle?