I like this solution from Ahmad M, a lot, but how do I add images in addition to titles, instead of replacing titles? (Sorry, I'm still pretty new to PHP and Stackexchange).
I mostly figured it out. I'm using Ahmad M's filter but needed to add ".$menu_object->title" to the thumbnail so now it looks like:
$menu_object->title = has_post_thumbnail($menu_object->object_id) ? get_the_post_thumbnail($menu_object->object_id, 'full') . $menu_object->title . : $menu_object->title;
Now my challenge is that I only want to add it to third level menu items (child of a child of a parent).