Beddings of all types have the potential to be dusty. And dust can trigger chronic breathing problems in horses, such as equine asthma (also called heaves). So, what is the best bedding for a horse with a respiratory condition? None at all, because those horses are best kept out of stalls entirely.
The number one recommendation from veterinarians is to keep horses prone to heaves outdoors continually, in the fresh air and well away from all dusts and particulates associated with an indoor barn environment. And the recommendation works—numerous studies have confirmed that living on a pasture is far better for heavey horses than indoor living with any type of bedding, forage or intense management. (The notable exception is horses with pasture heaves, who are triggered by molds, but these are a minority of cases in very specific, humid southern locales.)
Of course, if a horse with breathing troubles must be kept indoors for any period of time—say, to recover from a serious injury—you’ll want a bedding that is as dust-free as possible. If you can see any lingering dust in a sunbeam after you bed the stall, the material is too dusty for a horse with respiratory troubles. You might have to purchase very expensive, high-quality shavings or straw for just that specific horse or import a bedding that is otherwise hard to find in your area. Your veterinarian can help you locate a suitable bedding. The effort and expense will be worth it to protect your horse’s respiratory health while the rest of him heals.