Unless you are willing to train that dog, please don't crack it with a whip.
Correcting any dog with a harsh means without proper training techniques to back it up will only create a mean streak in the dog. Period. It takes more than just whipping a dog with a crop to learn something.
Border collies are smart and cunning. All you will manage to do is make it distrust you. Not your horses. The dog will run from you or will decide to one day take you on. And an unaltered female will be worse.
If you want the dog to learn to respect horses, the horses have to teach the dog to respect them with force, or you have to spend the time working as a dog trainer to teach the dog inappropriate behavior and REWARD the appropriate behavior.
You can't do only 1/2 the job and expect positive results.
I will say this. I find it funny how many people in this thread condone using an object of any sorts to hit or whip a dog, without appropriate training but would throw a gasket if you said you used a martingale to teach your horse head position. Not to mention the amount of discussion on this forum about "natural horsemanship" and appropriate training techniques.
Border collies have a dna makeup that gives them a lot of confidence and are very extraverted dogs. They are not the typical "guard dog" but they have a lot of the similar characterists of dogs bred to protect and serve. These dogs, in my opinion, are worse. True guard dogs are bred to attack based on man's command.
Most herding dogs will attack if they feel threatened or if their "charges" are threatened.
If this was a pitbull, rotweiller, or mastiff, would you approach it and start whipping it with your crop? Or would you think about the flip side of the dog's reaction?
Based on your posting, this dog has feral (herding) instincts and does not respect humans. I wouldn't take the chance myself.
I'm sorry, I don't mean to be negative, but your suggestion will not work effectively.