Count posts on multisite with blog id

In order to use wp_count_posts() as you would on a single site, pass the blog id into the switch_to_blog() function before calling wp_count_posts().

Example:

function wpse_get_post_count( $blog_id ){
    switch_to_blog( $blog_id );
    $post_count = wp_count_posts();
    restore_current_blog();
    return $post_count;
}

Ensure restore_current_blog() is used after every switch_to_blog() or you will risk difficulties mentioned in the notes section of the documentation and this WordPress Stack Exchange answer.