Actually, something is being left out. I do not remember him saying do not feed in the winter at all. He was more temperature specific than that. He said if the Koi are moving and swimming that they are using energy and they may need a little food. He said if you feed you must feed very little. Now if you are in a very cold region and your Koi go dormant then you must not feed at all.
His four season approach is as explained above though. Further clarification would be that the Koi should not be fed during the winter (you should base it on your temperatures), fed some, but not too much in the spring because this food would go to egg production and then during the summer growing season, July to October, they must be fed as much as they want. If you feed this way then you will get very good growth and have healthier Koi.