You’d need to change the generated widget markup created by register_sidebar in functions.php from:
'before_widget' => '<div id="widget_sidebar" class="widget-area">',
to something like:
'before_widget' => '<div id="widget_sidebar" class="widget-area %2$s">',
In theory, this would add a class ‘widget_text’ to the output that you could then use in your CSS.
Esmi that theory totally works! Thanks!