1st installing to an external drive is very possible and works and requires:
your bios support booting to the externel drive
and hmm there was something important i forgot .. umm sometimes it also depends on the externel drive you are trying to use

ex: i have booted, and run Fedora Core 4 off a externel
80GB USB drive

to successfully install it, it requires advanced install, .. NO Default options!
so most likely you didnt do this but here's what you have to do:
turn externel drive on
boot install cd/dvd
start the installation, and there's three important parts
1. do a cutom install, not an upgrade, not a default install
2. when you get to Disk Druid set it up yourself and make sure you select your external drive (ex: /dev/sdb) .. you can do LVM or a /boot / (root) swap .. well really any setup but be sure you select your externel drive
3. at grub install a screen should have a checkbox about advanced install .. you need that
we are trying to make grub install to the MBR of your external drive.
the next screen (advanced grub install) will allow you to install grub to internal or external.

the default install .. will not correctly do Druid or Grub because how is it supposed to know where you want Fedora installed when you have more than one drive.

so hopefully youve completed install, and you reboot to use Fedora from your externel drive:
grub should come up
Fedora will most likely begin booting and you will recieve an error "Kernel Panic" at least that's what I got, but that was FC4 so, kernel has definately come a way since than. but if you get it no big deal

reboot to Fedora rescue, automatically mount Fedora, chroot /mnt/sysimage
do:
mkinitrd --preload=ehci-hcd --preload=usb-storage --preload=scsi_mod --preload=sd_mod /boot/usbinitrd.img 2.6.15-1.2054_FC5
where that last series of numbers is kernel version

finally
nano /boot/grub/grub.conf
and change
initrd /initrd-2.6.15-1.2054_FC5
to
initrd /usbinitrd.img

reboot to your externel drive and hopefully fedora now works
___________________________
Steve
Dell Inspiron 9300 1.86GHZ Centrino, 1GB DDR2 533 dual channel, 80 GB Fujitsu PATA, Sony ATAPI DVD RW.
Dual Boot: Fedora 5 and Windows XP Professional SP2.
Built: 2 AMD computers both with ASUS motherboards, A8N-VM - socket 939 and M2N-E - AM2.