How to test if the widgetized area has any widgets?

I would use the is_active_sidebar() conditional:

<?php
if ( is_active_sidebar( 'footer' ) ) {
    ?>
    <div id="sidebar-footer">
        <?php dynamic_sidebar( 'footer' ); ?>
    </div>
    <?php
}
?>

That way, you can conditionally output the styled container itself.