It sounds like you are looking to change something about the HTML editor (TinyMCE by default), not so much the "Add Widget" page itself (but please correct me if I'm wrong).
To customize the HTML editor (TinyMCE), you would first need to override the
editor shape template for the Html
flavor. This shape template exists in the TinyMce module's Views folder, so you could simply copy that over. Then you'll need to modify this TinyMCE such that it accepts and handles dropped images.
When working on this customization, you'll want to work with the full source Orchard solution, because then you'll be able to discover how things such as the media library services are used by checking out the source code of that module.
A good example of how to customize TinyMCE is this module: