What month do you stop feeding koi? If I bought small koi at the end of summer would they make it in winter?

Are these fish being kept outdoors? Koi are best kept in ponds that are deep enough that they won't freeze solid. In the mid latitudes that would mean a pond at least 3 feet deep. If you are keeping your fish indoors and the water temperatures don't go below 50F then continue feeding, but make sure you have a very large tank. When the water temp goes below 50F quit feeding,also as the water temps drop reduce both the amount and frequency of the feedings. If you have doubts err on the side of less food.