Moses seemed fine while glowing,. It was those around him unable to handle it. He only wore a veil and only, it seems, after the problem was pointed out to him.
It's also interesting that when Moses spent time in the presence of God that his face was too bright to look at and he was forced to cover his face until the glow subsided. God walked with Adam and presumably Eve in the garden. Did they glow brightly all the time? Did the fall erase their glow thus enabling them to notice their nakedness?
