This expression "to win easily and comfortably" comes from horse racing.
Ordinarily, a jockey raises his hands to tighten his grip or use the crop to urge his mount forward. But if he is far ahead of the pack and victory seems certain, he may relax and ride with his hands down. This race slang passed into general use around 1900.
This word for "Nonsense!" probably comes from the building trades, where carpenters used feathering strips for roofing and siding houses.
Rows of clapboards were laid edge to edge to provide a flat surface over which new siding could be applied. These house feathers may have been called horsefeathers because of their large size.
The sense of "ludicrous" would follow, because house feathering was a cruder method of roofing a house. The old siding was simply covered over, instead of being stripped off first.
Word expert John Ciardi has another suggestion for the origin of the word. "Perhaps the successive layers of new wood reminded one at a distance of the wings of a chicken," he explains.
This root is not something a horse eats. It doesn't even look like a horse or its parts. But it is coarse.
Years ago, "horse" was used as an adjective to indicate something large and strong, as in a horsemint, horse bean, and horse mackerel.
Anyone who has eaten a horseradish knows that while it may look somewhat like the common radish, its texture and flavor are much, much stronger.
'Dictionary of Word and Phrase Origins,' by Jordan Almond; 'Horsefeathers,' by Charles E. Funk; 'Have a Nice Day,' by Christine Ammer; 'Brewer's Dictionary of Phrase and Fable,' by Ivor H. Evans; 'The Encyclopedia of Word and Phrase Origins,' by Robert Hendrickson; 'A Second Browser's Dictionary,' by John Ciardi.