Well, it is possible to install an operating system on an external drive, like Will said, if it uses USB it is possible, but I wouldn't recommend using USB, since it won't be as fast as a regular hard drive.

So you can't really get the usual speed from that operating system. I'd say its best to put the operating system on a normal internal drive and keep all the files on the external one, since the operating system itself (if it is a fresh install) won't take all that much space.