We're working with Samsung to see why the YouTube app isn't loading on Smart TV models. If you attempt to load the app and you get stuck at the YouTube logo (and possibly a little Flash icon in the corner), then this is the thread for you.
If you could take a moment and give us your software and app versions, I can pass this to Samsung:
S/W version : Menu - Support - Support information - S/W information(menu name may vary)
App Version : Smart Hub - Info button on the YT app