AFAIK MS Windows does not support booting from an external USB hard disk. Special version, possibly stripped down or hacked, has been sold on USB pen drives.
For a standard product you can install it. It just won't boot.
Curiously I am using an external hard disk running XP and have just put Vista onto it, together with 9 Linux. It is on a 500Gb eSata disk.
I could install most of the Vista onto it but it didn't complete or boot. So I installed it onto an internal Sata, cloned the partition across, remove the internal hard disk and now it boots and operates as all the other systems.
An eSata is actually an internal hard disk but placed outside the PC connected by an eSata cable. The mobo has to have an extra special socket in order to provide the eSata support.
So far I have found most Linux can be booted from an external USB hard disk. Non-Linux systems are only FreeDos and PCBSD as showed here.