I am very happy we do not have this requirement where I live. I believe it is even specifically stated somewhere for us that you aren't expected to use a mask while outside exercising. I would think that as long as you are adhering to social distancing requirements, you're good.
It is already a bit of a pain for me wearing one while walking up and down stairs at work, and I do not have problems with running out breath. Wearing a mask does take it out of me a bit though, so I can't imagine having to run with one.
Even with requirements in some states, there are exceptions, like having COPD, or other respiratory ailments.
From CNN: "There are few exceptions, though people who can't wear masks for medial reasons are exempt."
I consider myself exempt.