I did the following:
Add the following in your wp-config.php:
define('COOKIE_DOMAIN', 'yourdomain.org');
define('COOKIEPATH', '/');
You can make the path more specific (e.g. if your external script is in /myscript/ and your WP installation is in /myscript/wordpress/, then you can use ‘/myscript/’ as COOKIEPATH).
And then in my external script:
require_once('wp-pos/wp-blog-header.php');
if (! is_user_logged_in()) {
...
}