This is not possible in IE. They do not allow styling the drop-down component of the list, with the exception of the text inside it (i.e., Red Text).
IE actually uses a Windows-level control rather than a browser control, so it is rather limited.
Change When this message was originally made, a stable version of IE8 has not yet been released. According to comments, IE8 supports border styling. However, even ~ 2 years after the release of IE8, you still should not count on all your users who have IE8 +.
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