If it isn't locked, you most certainly should be able to. You said you're trying to 'drag' your skills. I'm not sure if you're literally clicking and holding, but perhaps you should try just left clicking once to bring them to your pointer. Then you can move them elsewhere and click again to drop them.
You can do the same thing from your skills menu (accessible by pressing K). Left click once to bring it to your pointer, go to your hotkey bar and left click again to drop it on the number of your choosing.
I hope that helps! ^_^