add-field-delivery-field-in-email.php

<?php

add_filter( 'woocommerce_email_order_meta_fields', 'add_delivery_date_to_emails' , 10, 3 );

function add_delivery_date_to_emails ( $fields, $sent_to_admin, $order ) {
    if( version_compare( get_option( 'woocommerce_version' ), '3.0.0', ">=" ) ) {            
        $order_id = $order->get_id();
    } else {
        $order_id = $order->id;
    }

    $delivery_date = get_post_meta( $order_id, '_delivery_date', true );

    if ( '' != $delivery_date ) {
	$fields[ 'Delivery Date' ] = array(
	    'label' => __( 'Delivery Date', 'add_extra_fields' ),
	    'value' => $delivery_date,
	);
    }
    return $fields;
}