When I lived in Colorado my big guy never was in a stall. He had a run in shed, but it snowed 400 inches plus several years in a row and he beared it all with a thick, fuzzy coat. I had a hammer in the barn to break the ice off his hooves. Horses are tougher than you think!
That being said, without a run in shed I would put him inside, too. In one of our pastures we use an old hay tent for a shelter. Makes them look very 'desert like'. The horse should have a choice to seek shelter and not be forced to sit out in the wind and pelting rain. Mine are always standing in the tent or run in when the weather is not so nice.