Is Toru Hagakure constantly naked? She seemed embarrassed to go barefoot and to be watched when she took her boots and gloves off. Since we can see when she is wearing those pieces of clothing does this mean she is constantly walking around naked?
Well, yes.

We know she can't make anything she has on her - including her clothing - invisible, so if she's totally invisible she's naked. We've seen her taking off her battle uniform (yes, the gloves and the boots) for tactical advantage.