Can you add editing of the Horizontal menu on Dashboard?

At the moment there is no way to edit the Toolbar (AKA “Admin Bar”) with this plugin. While it may contain some of the same links as the main admin menu, internally it’s an entirely separate thing and editing it will require a separate plugin/extra code.

You might find these posts useful:
https://sumtips.com/2011/03/customize-wordpress-admin-bar.html
https://www.doitwithwp.com/customize-wordpress-admin-bar/

Thanks for the links. The following worked to remove the New Post link:

<?php
function remove_admin_bar_links() {
	global $wp_admin_bar;
	$wp_admin_bar->remove_menu('new-post');
}
add_action( 'wp_before_admin_bar_render', 'remove_admin_bar_links' );

?>