If you want to add a specific PATH to the default PATH of your "root" account when using sudo, or sudo -i:
With Ubuntu 10.04.x LTS:
Modify accordingly both the /etc/environment and the etc/login.defs files.
With Ubuntu 12.04.x LTS:
Modify accordingly both the /etc/environment and the /etc/login.defs files as well as the line Defaults secure_path of the /etc/sudoers file (using visudo).
If you're using a GUI and aren't comfortable with the nano editor in text mode, use the following command to edit the /etc/sudoers file with gedit:
sudo EDITOR=gedit visudo
When you'll save the /etc/sudoers file, visudo will check the syntax of your modifications.
If all is OK, you'll go back to the terminal session.
If there is an error, press the letter "e" to edit the /etc/sudoers file again and correct your modification.
I didn't try with Ubuntu 12.10 yet but I guess (and hope) it's the same thing than for Ubuntu 12.04.x!