Change cursor type on input type="file"

Simple question... How do I change the cursor type on a file input type?

I've tried the following:

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html>
    <head>
        <style>
            input[type="file"] {
              cursor: pointer;
            }
        </style>
    </head>
    <body>
        <input type="file">
    </body>
</html>

For some reason, it won't play ball.