I actually have the opposite experience with my exercise-induced asthma.
It's quite dry and cold where I am currently, due to winter. Wearing a cloth mask increases the temperature and humidity of the air I breathe when working hard, and makes it less likely that asthma will be triggered.
It's a significant enough effect that I will sometimes wear a cloth mask specifically for this effect when doing something strenuous outdoors.
That would probably be true if we lived somewhere with actual winters. My daughter's PE class is in the afternoon, and the lowest high-temperature we've had all winter is 63.
It turns out a good fitting mask is essential for comfort. I had a problem with masks being hard to breathe in and fogging up my glasses. Then I found a good set of N95 masks that have a real solid fit. It's loose and flexible enough to be breathable, and has a solid seal across the nose so moisture doesn't get near my glasses. You can tell it's a good fit because it deflates/inflates likes a balloon when you breathe.
I did manage to find sports masks I wear when I got the gym that do make it much easier to breath, although they fog up my glasses still so I take those off when I'm there.