How to make it obvious that you can drag things that you normally can’t?

My interface allows users to move things that usually have fixed positions in other applications, such as text boxes. What can I do to make it obvious to the user that they can move certain objects?

The ideas that come to mind are:

• Add a unique border around movable objects
• Change mouse cursor to a "grab-it" icon when hovering on the object's border

I want it to be obvious without the user already having the idea that they can drag things around.