Account on external HD
You have two options depending on your needs:


You can have you OS and all your data installed on an external drive and then boot from your external drive by connecting your drive, and booting your mac while holding the option/alt key and select your external drive
The second option is to move you home folder to the external drive; this is done by many users who have a combination of an SSD and a HHD but you can do something similar depending on your needs. Here is a very straightforward tutorial on how to move your home folder to an external drive