It turns out the new patcher has created some issues within the custom skinning community. A custom skin, like the one above. is something players install client side to change their personal appearance; other users would not be able to see the difference. Custom skins range from bland recolors to complete graphical overhauls of champion models, spell effects, and icons. It works by overwriting the default models in your installation folder and has flourished into a very strong community since launch. The new patcher system has completely changed how the game stores data and has rendered the simple drag and drop method of installing these custom skins obsolete. Our fellow summoner Ramnok created a thread about the matter which attracted the attention of hohums.
"We did not intentionally remove the ability to make custom skins however we need to change how patching worked to:
1) To fix issues preventing people from playing when they replace files and break the game.
2) To support replays and other features in the future.
As to why they don't work currently... that's an issue for the custom skins community to resolve. I can't give information on how."
- hohums, Software Engineer, via the official forums.