Most of the women in Egypt cover their heads, but you will find many women, especially the younger ones, who choose not to (it’s a personal preference). I find it funny that on TV and in store windows, the mannequins and models do not cover their heads, and, in fact, wear some pretty revealing clothing (for Muslim standards). There are plenty though that do cover themselves from head to toe, including hands and face. At the private clubs, you won’t see the women swimming (except one or two). If they are, I’ve seen them completely clothed (head to foot) in the water. I wear a one-piece and cover myself in a large shirt when I am walking around the pool.
As a foreigner, I tend to wear pants and short-sleeved shirts. In the heat, long-sleeved shirts are just too much for me. Shorts are off-limits though. I have worn long skirts that go past my knees. When I run I do wear shorts and sleeveless tops, but this is in a private sporting club. I get some stares but not too much. It’s just WAY to hot to run in long pants and t-shirt.