VS 2012 seems to distinguish between 'Solution Folders', which are only folders containing either other solution folders, or containing project folders. The drag-and-drop works (with my settings) only for the project folders, and no for the solution folders.
If I add a new solution folder, nothing happens on the machine. If I drag-and-drop a machine folder to the main Solution, it refuses to accept it. If I drag-and-drop the folder to a Solution Folder, I get an error message saying this cannot be done.
When dealing with a solution level folder that has been removed for some reason, and now needs to be added back, open the .sln file in a text editor like notepad++.
Find your "FolderName" in the section that looks like this...
Delete from "Project" to "EndProject" ONLY for the specific Project/Folder you're having trouble with.
You may get a message in VS2012 that says your solution has been modified by an external source. Choose the option to "Discard" your changes for the external changes. Lastly, add your solution level folder, and add your project(s) to that folder as existing items, drag/drop them, or copy and paste them, according to your preference.
Expand the "Project" item in the menu bar and select "Show All Files". Then locate the folder you wish to add in the Solution Explorer (folders that are not currently included will be light grey with a dotted outline instead of the usual solid icon) right click the desired folder and select "Include in project"
Once finished select "Show All Files" from the Project menu again to return to the regular view.
(This is very similar to Radenko Zec's answer, but does not require the "Show All Files" button to already be present in a toolbar. I would just leave this as a response to his answer, but I don't currently have the reputation to leave comments.)
For those who had a hunch it could be done but weren't able to do it, NOTE:Drag Folder or Files ONTO the name of the Project Name in Solution Explorer in the least