As long as Koi (and all other fish) are alive they will eat. The feeding frequency and amount eaten at any one time will decrease as water temperature decreases but feeding does not stop. In their natural habitat, they still feed on periphyton and detritus during Winter months. Some nutritional intake is required to maintain even the low metabolic rate induced by colder temperatures. Without access to some form of nutrients, the fish are forced to utilize energy stored within their bodies which can result in a further weakening of their immune system beyond that normally caused by lower metabolism.
If your fish will eat, as Sissy alluded to, feed them. Just feed them less.