Even if she didn't have her wings, no one would doubt her angelic origin.
The grass growing around the lake covered her nosebleed-inducing birthday suit. Even if people are standing in the only access path, the tall grass would still provide enough cover for the girls to shower without worries.
Luna stepped further into the lake, she created ripples that reached the center of the lake.
The lake isn't particularly deep. The deepest area of the lake only reached Luna's' shoulder. Since Luna's wings absorbed water, she would sink if the depth of the lake is taller than her.
She rubbed her shoulder, collarbone, and her bountiful mountains. Luna continued washing herself down. It seemed like she was taking a bath seriously.
However, her eyes were not focused.