Yes it can be done and it is easy:
1.) Make sure you have at least 40GB HDD with no partition.
2.) Required OS is to be installed on it.
3.) Reboot your PC and enter the boot menu and choose to boot from the external drive.
4.) Make sure there is no previous windows on your PC, if it is already:
- First, install the windows on HDD and re run the windows installation and format your PC
- Note/Caution = Donot reinstall the windows on your PC's HDD.
4.) Then your PC will be booted from your HDD and there you go, you are done with an external OS.