I want to make some changes if the chosen payment method is COD. On existing WC_Order i have used
($order->payment_method_title == \'Cash On Delivery\' ? ...
The post meta key for the payment method ID is simply _payment_method
So if $order->payment_method
doesn't have the magic methods in place to get that automatically, you could retrieve the post meta using traditional WordPress
get_post_meta( $order->id, '_payment_method', true );
Update for WooCommerce 3.0
$order->get_payment_method();