TL;DR - It was fine, though I know my limits. Test in safe place if you want to try. Biggest issues are condensation making the mask slip down and finding a way to cleanly pack it away.
Although I'm lucky to have a rail trail in my city, I have to ride beside vehicles for most of the trip to get there. This includes getting over some fairly substantial hills which obviously makes me breath quite heavily. Usually I would run out of breath on the second hill and have to take a break, but recently I've also been having coughing fits. This might be psychosomatic as I've learned about how bad exhaust fumes are for your health (thanks NJB). Regardless, I started wearing a cheap respirator from the Orange Box store.
Certainly it makes it more difficult to breath, but for me it's a net gain. No more coughing fits, I can make it over that second hill and the dummy in the massive cope-wagon doesn't bother me as much.
The only trouble I have is packing it away once I get to the trail and the moisture from my breath builds up in the mask so it starts slipping down my face and blocks my nose. I think I'll have to get a more expensive mask to solve that issue.
As a disclaimer, I've been in the cadets and have years of martial arts training, so I know my limits. I suspect some people that try to wear a respirator while cycling might pass out, which is not a good thing to do when the people beside you are putting their convenience over your health and safety.
Stay safe (and healthy) out there.
Yes, it covers my big nose.