Disclaimer: neither of my kids have official diagnoses of "asthma".
That said, both of my kids have been 'diagnosed' with RAD (reactive airway disease) which is sort of like a precurser to asthma. It worsens significantly with colds and it may be most likely that they have virus-induced asthma... this means that when they get any sort of cold/upper respiratory infection, they wheeze like mad with a croup-like cough, and it can last days to weeks.
Both kids have ventolin rescue inhalers and nebulizers, just in case. They use them really infrequently, except in winter months
Doc has instructed us to do a nebulizer treatment before gymnastics practice and to monitor activity when they're wheezy, and to use my instincts in keeping them home when necessary. I think I've had my DD miss a total of 3-4 practices over the years due to her asthmatic symptoms alone, but again, it's hard to estimate that as it's always coupled with something upper respiratory... so 50/50 when I do keep her home whether I'd consider it "asthma" or "illness" (of course either of them would stay home with any fever or moderate-heavy bronchitis automatically, anyway, so I wouldn't attribute those events to asthma). DS has (knock wood!!) not been sick this way in some time, so it's not yet been an issue.
Thankfully, as they age, they're immune systems have strengthened, so there have been fewer colds, which means less wheezing, thank goodness.
For some perspective, DD has been in gymnastics for roughly eight years, has competed for 4 seasons, and currently trains 15ish hours per week. I always worried about the amount of chalk dust in the gym, but it hasn't seemed to be an issue. She does seem to tire out more easily than teammates sometimes, especially when sprinting, etc, but she usually does her best to keep up and has never left mid-practice.
For awhile she was doing 4-hr practices and that was rough on her (she'd even get headaches then), but she's been doing 3-hrs for awhile and has energy to spare when she's done.
(And, both of my kids have allergies, so it's likely they'll eventually get an asthma diagnosis, doc was just cautious to slap the label on them for insurance purposes... with ACA, it's becoming more likely they'll get the dx).