dumycode.php

<?php
// Frontend: Display the custom billing fields (in checkout and my account)
add_filter( 'woocommerce_billing_fields' ,'add_custom_billing_fields', 20, 1 );
function add_custom_billing_fields( $fields ) {
    $fields['billing_address_3'] = array(
        'label' => __( 'Stiege', 'woocommerce' ),
        'placeholder'   => _x('Stiege', 'placeholder', 'woocommerce'),
        'required'  => true,
        'class'     => array('form-row-wide'),
        'clear'     => true
    );
    return $fields;
}


// Save the custom billing fields (once order is placed)
add_action( 'woocommerce_checkout_create_order', 'save_custom_billing_fields', 20, 2 );
function save_custom_billing_fields( $order, $data ) {
    if ( isset( $_POST['billing_address_3'] ) && ! empty( $_POST['billing_address_3'] ) ) {
        $order->update_meta_data('_billing_address_3', sanitize_text_field( $_POST['billing_address_3'] ) );
        update_user_meta( $order->get_customer_id(), 'billing_address_3', sanitize_text_field( $_POST['billing_address_3'] ) );
    }

}
// This part does not work
// Backend: Display editable custom billing fields
function order_admin_custom_fields( $fields ) {
    $fields['address_3'] = array(
        'label' => __( 'Stiege', 'woocommerce' ),
        'show'  => true,
        'wrapper_class' => 'form-field-wide',
        'style' => '',
    );
    return $fields;
}
add_filter( 'woocommerce_admin_billing_fields' , 'order_admin_custom_fields' );