Food
Any fish in the wild would have a large variety of foods to choose from…plants, algae and small aquatic fish and animals… a balanced diet.  In our ponds they only get what we put in, along with a bit of algae and what might fall into the water. Therefore it's essential that we give them a well balanced diet using a variety of foods.
A good quality pellet food should be the basis of that diet, in my case I use Sho Koi. Pellet foods should have a minimum of 40% protein and have very little, if any corn in them, corn should be no higher than the third ingredient. After this, their diet can be supplemented using fresh seafood, (shrimp, herring, mackerel, squid, and mussels), Spirulina algae and calcium bentonite clay sprinkled on dampened food.
The use of Carbohydrates cereals, such as Cheerios, in the spring has been widely discussed and the general opinion is that they have very little nutritional value…so why not feed them something like chopped shrimp, where they can get some good protein.

The following is Bil Wight's Paste Food recipe and an essay on nutrition; I've added some of my own
comments as it goes along.
This is not just a recipe, but also goes into the whys and wherefores of feeding.
The amounts and ingredients are totally variable, and can be adapted to what you have available.  All the information, while as accurate as possible will not all apply to every pond, and common sense should be used in interpreting it.

A suggested simple ratio to start with might be as follows.

2 kilos  whole* herring, sprats or any other good cheap fish    
I've used smelts and mackerel and mussels in addition
The waste* from 2 kilos of prawns                                                        
Use shell, head, et all
Tentacles and waste* from 2 kilos of squid, or 1 kilo whole squid.      
Remember to take out the ink sac       
1 cup clay                                                                       
          A couple of teaspoons of  Spirulina Algae can be                                                                                                           added for fish over 3 years old.        
1 table spoonful yeast.
seaweed flour to thicken
(*Always remember, "Guts are good.")

Cook and puree all the fish, squid, prawn heads etc, and mix together with the cod liver oil.  Put 1 cupful of the mix back in the processor together with the desired additives. Process this while adding the seaweed flour till the right texture is achieved.  Mould into balls, bag and freeze. 
I don't cook any of the seafood, I slightly freeze it to make it easier to chop up in the food processor. When I use small boned fish, I leave the bones in and grind them up too...more calicum.

There is no need for a winter food and summer food.   (ie a carbohydrate rich winter food high in wheatgerm, and a higher protein food for the summer.)  If it's bad to feed protein in winter, why does "winter food" contain so much protein?
So called summer food can contain as much as 60% carbohydrate.
(If you read the labels on commercial foods,  carbohydrate is used as a binder, to hold the food together, fibre is irrelevant, and ash provides minerals.  In reasonably hard water, this too may not be important.)

As regards cold water feeding, again, opinion is mixed.  Some view it with horror, other view it as sensible to feed if the koi are willing.  If you are going to feed at cooler temps, the following should be borne in mind.  Make sure your biofiltration is excellent, rather than adequate, and test regularly to ensure that ammonia or nitrite isn't building up.  Large females that are building up egg masses are best starved for some of the winter to reduce the risk of their becoming egg bound.  However, the usual winter period where they show no interest in food is probably well in excess of this, and the average ponder is unlikely to need to worry about it.

One school of thought says what little carbo koi need, they can make from protein.  The other, that carp require 40% of their diet to be carbo.

This apparant divergence can, I believe, be eplained by the difference between the diets of wild and pond carp.  What carbo wild fish require, they will get from algae, water plants and, an important but often overlooked source, their live food.   A lot of live food contains carbohydrate based food in their guts, and this is a source of carbo for a lot of apparantly non carbo eating animals.

In a pond, these food sources are mostly absent or reduced to very low levels, and in the case of the live food, often low levels of variety too.  If fish in these conditions are simply fed fish derived protein, and nothing else, deficiency diseases and other dietary deficiencies will be a distinct possibility.

Most (not all) pellets contain a high % of carbo, which can reach as high as 50%.
This is usually derived from corn, wheat or soy, none of which can remotely be called part of their natural diet.  (There is a brand of pellet that uses algae as binder.)  I have no experimental evidence to prove this, but it is my opinion that it is not good to feed koi wheat, corn or soy based carbohydrates.  I think that this leads to cloudy water, clogged filters and fat fish, and I would prefer that my fish had, wherever possible, all their carbohydrates from algal sources.

A cynical view would be to point out that carbo is a comparatively cheap energy source compared to the more natural fish oils.  These provide energy in addition to being an excellent source of essential oils and vitamins.

In the spring, when the fish start to show an interest in food, conventional wisdom states that they should be fed a carbo rich diet to "awaken" their digestive systems.  However, if koi are given the choice between pellet, paste food or a high protein item like prawn tails, I have found that they will start feeding earlier and more aggressively on the prawn tails, and it is not until they have been eating these for a while will they start eating paste.  Even then, they prefer paste to pellet
.