I have a horse who has seasonal 'COPD' - not the best description for it, as it is seasonal but they don't tend to diagnose horses with 'asthma'.
I give her an inhaled steroid through a spacing chamber, which has a paediatric mask on the end. I place it over one of her nostrils and then block off her other nostril with my hand and then let her breathe in and out 3 or 4 times.
I start in March and will finish end of September and it keeps her very well controlled. However, when she does get break through symptoms, like coughing, I give her some ventolin and usually double her steroid for a week or so to get control of the symptoms again. Coughing is a symptom of the steroid not keeping the inflammation controlled so using both is a perfect solution, as sqad said.
I have specialised as a respiratory nurse in the past and the vet just let's me have whatever I need. I agree that most vets are not that sure about best practise for these sorts of problems!