Steam allows you to add a library to any drive connected to the system(Steam -> Settings -> Downloads -> Steam Library Folders). You may even be able to just move some games over to that folder after it is made, but I have not personally tried that way. You can do a backup and restore of games with the backup game files feature in steam(then remove local content and reinstall the game on the other drive).
USB 3.0 is fast enough for any hard drive on the market, but some externals will have the speed limited.
Now if this backup then restore does not appeal to you, see this link.
http://www.tomshardware.com/forum/294557-32-guide-move-software-games-drive-reinstalling
Please use it with case, it should allow a simple close steam and...