Just curious, does your brother already suffer with asthma? Does he take medications for it?
As a lifelong (medically diagnosed) asthma sufferer, I'm familiar with most of the triggers for the different asthma conditions. I speak from cause-and-effect observations, supplemented by copious amounts of reading on the subject and, of course, lots of discussions with physicians and asthma specialists. Geographic location and local conditions (what Larry calls "stuff") can have significant effects for some folks.
We've spent several months in WY, but at 6,000 feet, not the 8,000 feet of Burgess Junction. Speaking personally, altitude alone doesn't trigger asthma, nor does dry air per se. But cold dry air does, as does physical activity; Combining those two has (for me) a guaranteed immediate effect.
Larry gives good advice on staying hydrated, something we always warn visitors from "cool/wet" climates. They don't always heed the advice, and occasionally the paramedics are called.
Meanwhile, your brother might benefit from a discussion with his doctor.