Even then... the road is for VEHICLES and people riding horses do not have the right of way.
I'd agree with everything else you wrote except for the above. Many states have laws/traffic codes which require vehicles to yield to equestrian (and pedestrian) traffic, thus giving equestrians "right-of-way." Still other states have vehicle laws/codes which specifically prohibit doing something which might scare a horse and rider. While we can split hairs over specific situations of right-of-way, I would venture to say that equestrian traffic more often than not has the right-of-way.
That said, from the description posted right-of-way has nothing to do with this situation.
It is like anything else. If you and your horse cannot handle the road, trail, arena - whatever - then you are taking a calculated risk in riding. Even a bomb-proof horse can dump a rider for no apparent reason. If you ride at all, you run the risk of getting hurt. Unfortunately, some states still do not recognize the concept of "inherent risk," making it easier to start frivolous lawsuits.
As others have said, definitely avoid ALL contact or communication with these twits. ANYTHING you say can/will eventually be used against you. (i.e. "I'm sorry you got hurt" = you admit you caused the accident). Any information provided is too much information. Don't talk, don't write, don't say anything. Wait for a lawyer to contact you - if they can find one who is sleazy enough to take a case like this.
If/when you are contacted by a lawyer, you might consider starting with the insurance company which covers the vehicle you were driving. That's what you pay the insurance company for. At that time, it might also pay to consult your own lawyer. More than likely, the insurance company will take care of everything (probably by telling these people to take a hike).