It's not possible (short of recent hackers creating new firmware, etc)
The iPod nano, just like other iPods, needs music files to be transferred by iTunes or a compatible application - the files have to be put in precisely the right place, with the right database file and so on. You can drag MP3s (or any files) to the Nano for storage, but they won't play.
If that's a big issue for you, get a competing player rather than an iPod, lots of the competition will let you drag and drop.