The photograph above was taken half way through the run at Ironman Chattanooga last year. It was far from an easy run, so I know that I was breathing through my mouth. In training however, if I know that I have to keep my effort low, I use nose breathing to help ensure that I do that.
It is very difficult to run hard while breathing in and out through your nose. Therefore, if you force yourself to run while breathing entirely through your nose, you know that your overall effort will stay low and under control. This is a great tool for workouts that are prescribed at easy effort.
Nose breathing has other benefits too. The air entering your body is warmed and filtered. The resistance of nasal breathing, results in a lower air intake and this in turn, makes the body more efficient at oxygen uptake. You build up a greater tolerance to carbon dioxide and this helps oxygenation of the muscles.
It was very hot outside today, so I made sure to breath only through my nose on my run. This did indeed keep my effort (and pace) lower. I am glad I did keep my effort low, because I was really sweating by the time I finished. My body was clearly working hard, just to try and keep me cool. If I had run at my normal effort/pace, then I would have probably have been pushing too hard, which was not what my training plan call for today.