Using non-medical face masks during exercise does cause some minor discomfort, however, it appears to be safe when used by healthy individuals in short-term sub-vigorous intensities. Long term effects have not been studied.
Epstein, D, et al. found that;
"In healthy subjects, aerobic exercise with either a surgical mask or N95 respirator is safe and feasible. Although it may be associated
with some discomfort, masking has only minor effects on physiological
parameters during exercise."
Additionally, the above study noted no major differences in heart rate, respiratory rate, oxygen saturation, or RPE between the three trials (no mask, surgical mask, N95 respirator):
Figure 1: Mean changes in physiological parameters throughout the exercise test performed by 16 subjects without a mask, with a surgical mask, and with N95 respirator. A, Heart rate (beats/min). B, Respiratory rate (breaths/min). C, Oxygen saturation (%). D, Rated Perceived Exertion (RPE) Scale (score). Error bars represent 95% confidence interval
Similarly, Wong, A, et al. found that heart rates of participants were 3% higher while wearing a mask. By contrast, they found that reported RPE's of participants were 17% higher while wearing a mask. The study concluded a different finding from the previous stating that:
"The laboratory study to investigate the physiological effect of wearing a facemask found that it significantly elevated heart rate and perceived exertion."
"Exercise with a facemask definitely has a toll on the human body and it is advised to adjust the exercise intensity when masked."
With RPE being a self-reported factor, one could conclude that the psychological effects of wearing a mask while exercising are individualized, while heart rate is increased regardless. Increased heart rate could definitely be attributed to an increase in air flow resistance: "Previous studies found that the use of N95 respirators leads to a mean increment of 126% and 122% in inspiratory and expiratory flow resistances"1.
Both studies noted that exercising with a mask was generally uncomfortable with the face becoming more humid and warm. Neither study looked at these effects in detail. Additionally, both studies were conducted on healthy individuals and advise against exercising while wearing a mask if you already suffer from obstructive lung diseases.
Finally, this short report has some cleanliness guidelines. They suggest washing masks frequently to prevent the mask from becoming contaminated, using a more breathable material (when selecting a cloth mask), and using multiple masks if your mask gets too wet while working out (as breathing through a damp mask would be even more strenuous).
A bit of anecdotal addition: I have definitely noticed getting warmer and I have been going through more water than usual. I think this is just because I'm sweating more; like if I worked out with a hoodie and toque on. Breathing wise, I've realized that I am simply more aware of my breathing with the mask on. It seems like I'm breathing heavier but when I stop and think, I'm not, I just feel it blowing back on me. I've now done heavy squat/bench and dead/bench days as well as a cardio day while wearing a mask. It is definitely annoying but not at all life-threatening. Bring more water, keep the gyms open.