How to get body field within THEME_page_alter
According the hook_page_alter() documentation you should be able find the body like that.

$description = $page['content']['system_main']['nodes'][$nid]['body'];


But if you still have the problem you can display all data from your page with the help of Devel module or simply with a print_r($page); and look where is the content that you're looking for.