Maruju tell me they use sinking all the time to prevent food being washed to edges. In addition to pellets they will also use silkworm pupae at times.
Others clearly use floating as across the mountains there are feeding rings set up to contain the pellets to one area.
Some use auto feeders, some don't. Some use on demand feeders.
I've seen a number of different brands of food around the place, i'm unaware of a special 'mud pond' food.
The reality is that there are hundreds of breeders and therefore there are hundreds of answers, and even individual breeders will have different foods for different Koi throughout the season and will also adjust foods dependent on condition of Koi and pond.
This afternoon we were out touring a number of the farms mud ponds, myself, Hisashi Hirasawa (the boss) and Devin Swanson.
The food fed will vary from pond to pond, expensive Koi get expensive food, cheaper Koi get cheaper food!
Expensive foods, such as Saki Hikari only come in floating pellets.
Floating pellets are only fed to ponds which are well protected from the air, for 2 reasons:
1) ducks and such like soon get used to the sight, sound and taste of floating pellets and will outfight the Koi for them.
2) the sight of brightly coloured Nishikigoi engrossed in feeding attracts predators.
The ponds with the best quality Nishikigoi in them are the ones that are best protected.