Add custom meta field to WooCommerce order email.

functions.php

add_filter('woocommerce_email_order_meta_fields', 'dog_breed_checkout_field_order_meta_fields', 10, 3 );
function dog_breed_checkout_field_order_meta_fields( $fields, $sent_to_admin, $order ) {
    $fields['dog_breed_name'] = array(
                'label' => __( 'Dog Breed' ),
                'value' => get_post_meta( $order->id, 'dog_breed_name', true ),
            );
    return $fields;
}