How we install os in external hard disk
how to install os on external hard disk
If your motherboard bios supports USB boot devices you can do it, but it is not a real great idea.
The USB 2.0 connection is quite slow so you may want to use eSATA or USB 3 if you do proceed, although both of those will be significantly slower than the internal SATA ports. You would need to load the drivers during the Win 7 installation.
The other reason is that your external drive is not going to be portable between computers to run the OS unless they are very similar due to the driver differences and you will likely see more BSODs than you expect.
Is there a particular reason that you want to do this?