<p>I'm using tortoise svn in Windows.</p>

<p>How can I branch in SVN and have it branch my svn:external folders as well?</p>

When you create a branch within Subversion you are simply creating a cheap copy of the trunk, branch, or tag that you are branching from. This cheap copy will contain all of the same files and properties as the trunk, branch, or tag that you branched from until you begin to modify the properties or files of the new branch.
However, you may be able to modify one of the 'commit' hooks to modify settings automatically once you commit your branch.
http://svnbook.red-bean.com/en/1.1/ch05s02.html
Otherwise if you want your externals to be modified on the branch you will need to do so manually.