Custom Field sort not working (WP 3.8.1)

I think your query arguments are missing meta_key, which in this case should be 'event-date'. You need it outside the meta query for orderby to work. Try this:

$today = date("Ymd", strtotime(current_time('mysql')));

$args = array(
  "post_type" => "post",
  "post_status" => "publish",
  "posts_per_page" => -1,
  "cat" => 13,
  "meta_query" => array(
   array(
    "key" => "event-date",
    'type' => 'NUMERIC',
    'value' => $today,
    "compare" => ">="
  )
  ),
  'meta_key' => 'event-date', // meta_key added
  'orderby' => 'meta_value_num',                            
  'order' => 'ASC'
  );
  $eventsbody = new WP_Query($args);