The cold was certainly a trigger for our horse as well, but I'd still opt for lots of turnout with blankets (rugs). Air quality is your top priority with a horse that coughs. I live in eastern Canada so I know all about the cold, but my horse has done much better with 24/7 turnout in all kinds of weather - blizzards, freezing rain, hail, you name it. I do have open stalls though, so they can come in and out as they please, but the horses are almost never shut in. I'd turn out this horse as much as possible. They can take a lot more bad weather than we think, especially if they're blanketed.