I did this to move my sims games from one computer to another.
All you need to do is copy the Electronics Art folder, and paste it. Nice and simple!
Edit: Wait, sorry, I may have misread the question. What I answered to is how to move stuff onto the EHD as a backup or when moving it to another computer.
Are you intending to play it from the external hard drive? If so, the answer may be different - I've never tried it.
Sorry for the confusion.