Literally speaking, to be “shod” is to be “shoed:” that is, to be wearing shoes.
A shod horse is one that’s wearing shoes. (And a shod shovel, or a shod arrow, is wearing a “shoe” of metal.)
If a horse’s shoes have been roughly attached, with the nails poking out, then the horse is roughshod. (Here, for the sake of understanding the word, it doesn’t matter whether the installation was sloppily done or purposefully done to help the horse get a better grip on the ground. Either way, the nail heads are poking out.)
If you literally “ride roughshod over” something, or “run roughshod over” it, you’re riding your horse over it and pounding it with those nail heads that poke out.
If you run or ride roughshod over something figuratively, you’re treating it in a rough, cruel way.
So, roughshod things are rough and cruel, in a way that suggests riding over things on a horse with nail heads poking out of its shoes.
Part of speech:
Usually it’s an adverb, in phrases like “to run roughshod over” and “to ride roughshod over.”
Sometimes it’s an adjective: “her roughshod manners.”
None are in use. (Do you think we can make “roughshoddiness” happen?)
how to use it:
This fun-to-say word helps you express how someone’s bossiness, or someone’s disregard for things and people, has veered into cruelty and brutality.
We mostly stick to the (nicely alliterative) phrases “run roughshod over” and “ride roughshod over:”
“She runs roughshod over the customers.”
“He rode roughshod over the rules of these debates.”
“This is them running roughshod over the entire fact-checking industry” (Slate).
But you can also swap in your own verb: talk about, for example, walking, treading, or trampling roughshod over people, situations, and abstract things. Just keep to that basic metaphor of horseback-riding: you wouldn’t want to mix your metaphors by talking about, for example, “rolling roughshod over” something.
And it’s rare, but you can free this word completely from that phrase, and simply talk about roughshod manners, attitudes, behavior, decisions, management styles, etc.
“Yet I did not die. While I lay waiting to do so the insistent ache of my bones… slowly blurred me into apathy… Centuries trampled roughshod over me.”
— Charles Neville Buck; Chapter XI: I Find Myself a Demi-God, The Portal of Dreams; 1912
“(He was a dictator) who ran roughshod over the democratic freedoms of religion, speech, the press, assembly, dissent and protections from arbitrary arrest, imprisonment and death.”
— Joseph Betz, Fox News, 26 February 2020