This Is How/When You Change Skins

[Moon Rabbit]

You'll need to unlock Rama by finishing her mission. Return to the base. Then edit/change your squad members (switch members in/out) by hitting 'deploy'. In the squad selection window is the option to change your character's skins.

You can also access a Loadout window by going to the dark matter crystal in the middle of the base and following the stairs down into a basement like area. Which 'deploy' teleports you to if you back out of it without deploying.