Here is the deal...if you live in elk country and can hunt all the time you can afford a few risks like not wearing SOMETHING to hide your face. Out of state dream hunts are something else entirely.
As RC has said, a human face shines like a beacon in most light conditions. After sunset, before dark, I saw a man's face from 100 yards this fall while he was sitting still in the middle of a bush waiting to ambush ducks. (Stood out like a blazing beacon)
Cover your face with something...if you are sweating from the heat you MAY want to be hunting differently anyways. (think wallows, etc. places where it is cooler) I use a face mask or burnt cork no matter what. Elk are not as skittish as whitetails, but they aren't dumb either. Also, in the rut they will come from unexpected places and at unexpected times...Often you will have to setup on the fly and your face should not be one of your concerns in that situation.
Try both options this summer while shooting your bow and that will tell you which you prefer.