Hide payment icons on the checkout form when cart total is free
<?php
/*
 * Plugin Name: Easy Digital Downloads - Hide Payment Icons When Free
 * Description: Hide payment icons on the checkout form when cart total is free
 * Author: Andrew Munro
 * Author URI: https://easydigitaldownloads.com/
 * Version: 1.0
 */

function sumobi_edd_hide_payment_icons() {
	$cart_total = edd_get_cart_total();

	if ( $cart_total )
		return;

	remove_action( 'edd_payment_mode_top', 'edd_show_payment_icons' );
	remove_action( 'edd_checkout_form_top', 'edd_show_payment_icons' );
}
add_action( 'template_redirect', 'sumobi_edd_hide_payment_icons' );
To implement this snippet on your site, create a brand new, empty WordPress plugin and paste the above code inside.