How To Call WP_Query From A Subdomain?

Why don’t you try using the WP API?

You could then pull posts from a URL like this …

http://subdomain.example.com/wp-json/posts

You can also set custom post types to use the WP API and then access them also in a similar manner, you would need to add the following to your CPT args:

$args = array(
         //...
        'show_in_rest'       => true,
        'rest_base'          => 'books-api',
        'rest_controller_class' => 'WP_REST_Posts_Controller',
       )
    );

Take a look at: http://v2.wp-api.org/extending/custom-content-types/

You can even use WP_Query parameters like this:

http://subdomain.example.com/wp-json/posts?filter[posts_per_page]=2&filter[order]=ASC

You could use jQuery.getJSON() to get the data cross domain:

 $.getJSON('http://subdomain.example.com/wp-json/posts', function (data) {
    console.log(data);
  });