Forget the cowboys of the Old West: This expression comes from the days of knighthood in the Middle Ages, when young squires were given a pair of gilded spurs by their lords for their first deeds of valor.
Now the expression no longer means gaining footgear, but winning honor from one's peers for an achievement - which could be as gallant as getting a first sale, writing a book, or placing in a race.
Be glad that you are not living in the 17th century. Back then, riding roughshod over someone involved more than a lack of consideration.
The expression goes back to the days of cavalry, when horseshoes might have had projecting nailheads or points. These offered the horse better footing on slippery terrain, but they also served as an additional weapon should the cavalry encounter foot soldiers. Today, a person who acts without taking others' concerns into account may be said to "ride roughshod" over them.
SOURCES: 'Why You Say It,' by Webb Garrison; 'The Barnhart Dictionary of Etymology,' by Robert K. Barnhart; 'The Encyclopedia of Word and Phrase Origins,' by Robert Hendrickson.