Pass data to hook_preprocess_html from custom module
D7's html.tpl.php doesn't contain menu in $vars, as it's supposed to represent the template that contains the high-level HTML document. This data is in page.tpl.php via $main_menu / $secondary_menu vars.

If you need menu data in hook_preprocess_html() you can do something like call menu_tree_all_data('main-menu') in your code which will retrieve the menu data for main-menu.