Windows 7 on an external hard drive
The operating system is downloaded from the Microsoft site in the form of a Disk Image File (.iso) which is around 2.5GB in size for the 32 bit version. This file can be downloaded (it can take quite a while (hours) even on a DSL or cable connection) to anyplace, including an external drive. Remember where the file is located as after the download finishes the file must be burned to a DVD.
Installing the operating system requires booting on the DVD, following the instructions provided on the Microsoft site, and installing the OS on an available hard drive or partition on a hard drive. Although this may be possible to install on an external hard drive it probably would not be practical with an operating system of this size booting and transferring data via a USB port.
Most desktop computers allow installation of two or more hard drives and have the available wiring (data and power) for either IDE or SATA drives (or both). Granted, some cases require removal of both side covers to gain access to add/remove hard drives. Others have quick remove (no screws) side covers and hard drive slots that do not require mounting screws having one side sliding locking tabs to hold the hard drive in place.
With two hard drives installed (and wired) it is then a choice of which hard drive to boot from when powering the system. This works fine but there is no need to power and run two drives if you are just using one. If access to the wiring is easy, just swapping the power and data cables before powering the system for boot is an option. This decreases the power draw on the PSU, generates less heat/noise, and reduces wear on the drives. It also isolates the operating system to one drive.
While testing some Linux operating systems, which can run from a CD or USB jump drive, compared to having the same system installed on a hard drive there is quite a difference in response time. Linux systems are easy to run/test and can give older computers quite a bit of zip and new life. Some of the smaller Linux operating systems (Puppy Linux or Damn Small Linux) are only 50-100MB in size and can run with as little as 16MB of Ram. Others like PCLinux and Ubuntu will utilize a full CD around 700MB.