I'm pretty sure you can wear your own. I wear my own when i'm waiting around on the range and such, but you have to remember i'm not in a war zone. However, in the military you get some dicks who say "you have to have a chit (doctors note saying that you are required to wear sunglasses because if you don't your eyes will explode) to wear sunglasses." This happens on course all the time. But for those guys over there they have no problems customizing their kit and weapons, and wearing, to an extent, whatever they want that will make them more comfortable.
I do know the military provides snow glasses because I have a pair to protect the eyes from snow blindness, and they will also provide goggles and things like that for dust, but I don't think they provide sunglasses. So I don't think wearing your own is a big deal.