Not sure what Beth means about side affects ? Taking the 'micky' about steroids? Prednisolone isn't an 'anabolic steroid' like 'body builders', etc. take. If I get a 'bad chest', say a cold, I also take that, 8 per day.
If it's only Spring to Autumn you get symptoms, it may well be pollen that's a cause, but as you say being in the stables near the horses, causes problems. I'm inclined to think it may be more than just pollen. If I'm around pet birds or cats that is the first symptoms I get, if I stay to long after that I know I'll have an attack, or need to use preventer.
Re. antihistamines, that maybe a good idea, you can get them in tablet or inhaler form.
I hope you get it controlled, If not I'd ask to see another Dr. for a second openion.
I had to as the first one I saw, couldn't get my asthma controlled. The other, younger Dr was more informed and knew more.