If the code you have provided is the only code you are using to achieve what you want then thats incomplete code. Below is the tested version of code which works well. I hope this helps:
/* Add the field to the checkout */
add_action('woocommerce_after_order_notes', 'my_custom_checkout_field');
function my_custom_checkout_field( $checkout ) {
echo '<div id="my_custom_checkout_field"><h3>'.__('My Field').'</h3>';
woocommerce_form_field( 'p_trade', array(
'type' => 'select',
'class' => array('p-trade orm-row-wide'),
'label' => __('Trade Details'),
'placeholder' => __('Enter a number'),
'clear' => true,
'options' => array( 'trade-1' => 'Trade One', 'trade-2' => 'Trade Two', 'trade-3' => 'Trade Three', 'trade-4' => 'Trade Four' )
), $checkout->get_value( 'p_trade' ));
woocommerce_form_field( 'p_retail', array(
'type' => 'select',
'class' => array('p-retail orm-row-wide'),
'label' => __('Retail Details'),
'placeholder' => __('Enter a number'),
'clear' => true,
'options' => array('retail-1' => 'Retail One', 'retail-2' => 'Retail Two', 'retail-3' => 'Retail Three', 'retail-4' => 'Retail Four')
), $checkout->get_value( 'p_retail' ));
echo '</div>';
}
/* Update the order meta with field value */
add_action('woocommerce_checkout_update_order_meta', 'my_custom_checkout_field_update_order_meta');
function my_custom_checkout_field_update_order_meta( $order_id ) {
if ($_POST['p_trade']) update_post_meta( $order_id, 'p_trade', esc_attr($_POST['p_trade']));
if ($_POST['p_retail']) update_post_meta( $order_id, 'p_retail', esc_attr($_POST['p_retail']));
}
/* Add the fields to order email */
add_filter( 'woocommerce_email_order_meta_keys', 'my_custom_checkout_field_order_meta_keys' );
function my_custom_checkout_field_order_meta_keys( $keys ) {
echo '<h3>Payment Option:</h3>';
$keys['Trade'] = 'p_trade';
$keys['Retail'] = 'p_retail';
return $keys;
}