I know nothing about CF and riding (I have asthma, but won't compare apples to oranges). So instead, I googled "CF blog horse riding" (because there seem to be no shortage of CF blogs out there), and got several hits, mostly UK, but still a place to start. "cystic fibrosis horseback riding" also turns up a few results. Most of what I found has to do with children, but seems applicable to adults as well.
I don't have any direct experience but I grew up with a friend who had CF she was in pony club with me and rode for years. She jumped and did everything we did. She even attended camp which was held in an old cow barn. One of the mothers was a nurse and offered to come to camp every morning to give her the PT she needed. She was on some serious drugs. As she reached around age 14 her condition became significantly worse and ultimately she had a heart and lung transplant. In fact she was one of the first people to ever have a heart and lung transplant. She came back to riding although was never as proficient as she had once been. I have vivid memories of her riding with oxygen the tanks were hung from the front of her saddle. She owned and looked after her own pony (all be it with significant help from her family). She ALWAYS rode with the rest of us kids and had a blast, it was one of the few things that kept her going. It was a truly wonderful thing for those of us leading normal lives to be around her and probably visa versa. Sadly Pippa died in November 2001 I think she was 24 or 25. She had beaten many of the odds placed against her and achieved many things that people said were not possible for a child with CF including going to university and getting a degree. So never say never.
Thank you for the leads KLS, I don't know why I didn't think to ask Mistress Google!
Equilibrate, you were indeed lucky to be exposed to so determined a soul. My SO is quite old for a CF'er at 35 (!!! his parents were told not to expect him to live to be 6 months, a year, five years etc !!!) And I am thankful he is so much stronger than I think I might be with his challenge. Pippa sounds like a kindred spirit in many ways to my guy, he never quits anything he puts his mind too.