You can't just boot an ISO file from an external disk, or pen drive. You have to give the disk a boot sector and it needs to know how to read the files.
Have a look at: http://unetbootin.sourceforge.net/
This bit of software allows you to put the files from an ISO boot CD image onto a USB pen drive, it should also work for a USB HDD.
Now the hard part... If you boot from a drive then you will not be able to complete the install to the same disk without removing the very option that allows you to boot that disc in the first place. ie. When you install it will replace the boot sector and associated boot info with the one for the OS you are installing.
The other issue here is performance. USB to HDD is a VERY slow interface. Now it's bad copying files one way but when installing the sequence would be:
1. Copy file from USB to PC ram
2. Expand archive
3. Write back to USB device
So for a 700Mb install you could well end up sending a few GB of data over the USB interface, add in the CPU time and the install will take forever to run.
Some Live Linux systems allow you to store state, puppy for example allows you to have a pendrive with the .iso installer on which will live boot. You can then save your bookmarks for example into a file that it hold on the same pen drive, it does not however have an installed copy of the OS. This is not the same thing as an installed copy of the OS in terms of Ubuntu.
My suggestion is this.
1. Create a USB pen drive for the install media or use a CD
2. Don't bother formatting the HDD, this can be done at install*
3. Install in the standard way.
*in terms of file format you have some options. Either install your Ubuntu on a FAT32 file system which Windows can read fine but which does have a file size limitation of 4Gb, not great if you play with DVD images (BTW the next Ubuntu will be a DVD edition although likely only ~1.5Gb in size).
The other option is to use EXT2/3 for the disk format and then install EXT2 IFS on Windows (http://www.fs-driver.org/) This will then allow you to read EXT2/3 file systems as if they were local drives on Windows.
If you want a file system that Windows will really struggle with then ReiserFS, ZFS and a few others are not well supported. It depends what sort of security you want, there is nothing stopping you encrypting the whole disk with Crypt, but again it's not going to be fast over USB.