Horses get broken winded after having a severe allergic reaction of the chest (like a bad asthma or COPD attack). The inflammation in the lungs causes a lot of damage to the insides and this damage stops the airways staying open during the normal process of breathing. This means that a horse that is broken winded has to take much more effort than normal to get air into its body. It becomes so difficult to breath that the stomach is used to try and open up the lungs more at each breath. This gives rise to the typical sign of ’double breathing’.
Broken windedness tends to happen when a horse for example has had an allergic reaction to mouldy hay but the mouldy hay is not taken away quickly enough and the damage keeps on getting worse and worse until it becomes irreversible. No drugs seem to make much of a difference in such situations and the horse has to live with the problem with some temporary help with drugs like steroids and ones to keep the airways open artificially.