I do want to clarify my post...not feeding fish in winter doesn't mean no problems. Fish can survive the winter without food if they they're in good shape, been well fed in the warm months, put on weight, water was in good shape, etc. Koi require a lot of food in warm months to put on weight. I think many Koi in Water Gardens aren't fed very much in the warm months, maybe just once or twice a day. It's not a perfect situation to get to winter and then ask how the Koi should be fed. The horse is already out of the barn and down the road. When the water is cold they just don't grow very well or put on weight because their metabolism is so slow so feeding doesn't really help them any when compared to the downside of water quality. Taking stressed under fed fish and then throw ammonia at them is probably not a good thing.
I don't know the details in this case of course, never do.
I just think if a Koi owner is asking as basic a question as whether to feed in winter that they probably aren't testing water parameters either, so the safest suggestion is to stop feeding. But Koi are pretty tough, they might be able to get through winter with some ammonia so feeding them isn't the end of the world. And we're probably not talking about expensive fish so easy enough to replace any in the spring. When a Koi cost $2,000 people seem to take more interest in care.