Snippet to add description to WooCommerce shipping methods

add-shipping-method-description.php

<?php

add_filter('woocommerce_cart_shipping_method_full_label', 'custom_shipping_method_label', 10, 2);
function custom_shipping_method_label( $label, $method ){
    switch ( $method->instance_id ) {
        case '7':  // Replace with your own shipping method id
            $text = '<br /><small>' . __('Add Method Description') . '</small>';
            break;	
        default:
            $text = '';    
    }
    return $label . $text;
}

?>