It's not true that all horses have feathers. They all may have 'feathers' (as you said, note the '') but those are NOT feathers even though people like to call them so.
"Feathering, or feather, is a term used to describe the long hair on the lower legs and fetlocks of some breeds of horse and pony. On some horses, especially draft breeds, the hair can almost cover the hooves. While nearly all horses will grow longer hair on the lower legs and back of the fetlocks at times, particularly in the winter, "Feather" refers to the particularly long, luxuriant growth that is characteristic of certain breeds."
Another very interesting thing I never knew before was that feather is a recessive gene. I found a few articles about this.
"Feather is a recessive, and it is accumulative. If you breed a feathered horse to any non-feathered horse, you DO NOT get a feathered horse."
(About a drum horse) "Many times people ask the GCDHA if they can register a horse that is a non-feathered spotted draft. The answer to that question is no; the horse must be a blend of one or more of the above mentioned feathered draft breeds because feather is a recessive gene, and a mark of the Drum Horse breed in America. The only way to preserve the heavy feathering of the Drum Horse is to breed feathered horses to other feathered horses. Breeding a smooth legged horse to a feathered horse will result in a smooth legged or lightly feathered horse, which would not meet the Drum Horse registration requirements."
I will not go into details and start polemizing about where's the border between "feathered" and "non-feathered" as officially even Friesians aren't a feathered breed but one definitelly can't say that every hrorse has feathers.
Unless there is a difference between the terms "feather" and "feathers" which I'm not familiar with...