The most recent edition of The New York Times' "Ask Well" column investigates this very question. In an interview with Dr. Oliver Jay, director of the Thermal Ergonomics Laboratory at the University of Ottawa in Canada, Times journalist Gretchen Reynolds delves into the truth behind sweating it out. Dr. Jay states that "sweating, per se, provides no health benefits." Rather, it's simply the health benefits of strenuous exercise that lead one to feeling better after a hard workout.
And, what about the idea that sweating is good for your skin? It's true, though the reasons are a bit nuanced. It's thought that sweat could contain a natural antibiotic known as Dermcidin. This might play a role in killing off acne-causing bacteria on the skin. Sweating also opens the pores in the face — much like a facialist might accomplish using steam — and this can allow trapped oils to escape before it results in breakouts. The caveat here is that sweat must be removed from the body and face as soon as possible after a workout or else you run the risk of developing miliaria, red bumps that develop when the sweat glands become blocked.
Also, of course, you need to replenish whatever water has been lost through exercise. So, while sweating might not be the cure-all some claim it to be, it will likely give your face a little glow. Time to sweat it out!