Do not drag the Photos folder. This is a system folder and that's probably the reason you get the error message. Instead, go to the real source folder, select all subfolders containing the pictures you want to move, right click on the selection, click on Properties to check again the total size of the selected folders, close the properties window, right click again on the selection, click copy, then go to the external hdd, right click on the folder where you want to copy the files and finally click paste.
Dragging a system folder can have unforeseeable results. I almost never use the drag/drop facility, but usually only copy/paste.
Regarding the format of your hdd, nowadays it is best to have it formatted as NTFS in order to be able...