Koi will eat both animal and vegetable matter which makes them omnivorous.  They do not have stomachs so they can not eat a large amount of food at one time. 

This is the reason Koi spend a great deal of time foraging around for Koi food.  They will actually eat just about anything that is small enough for them to swallow whole.

A Koi's metabolism functions best at temperatures above 70º F. High protein foods are difficult to digest when the water temperature falls below 65º F. In water temperatures below 65º F but above 42º F feed wheat germ based foods to your koi and goldfish.

However, Koi still need sufficient carbohydrates for energy when water temperatures are low. This is particularly true for Koi less than 1 year old.

Koi do not have a stomach.
Feed smaller quantities more frequently for better nutritional absorption.

Feed only as much as the fish will eat in about 3 to 5 minutes.