That's what we do. While driving we are supposed to follow the traffic laws. But walking with or without horses if cars are coming I just cross to the other side to give them room and walk in the direction that would be against traffic.
Marsha, you are doing it correctly, IMO. While carting you should be moving in the direction of the traffic, like a bicyclist should do. While walking your horse, you are a "pedestrian" and should be facing the traffic.
I've tried to explain this to my sister and others who walk horses with me but they refuse. Then we end up walking on both sides of the road, which is a hazard to traffic. I guess because I was a pedestrian for so many years, it is natural for me to walk facing traffic. People who have never had to walk anywhere only think about driving. It seems weird to them to face traffic.
Very walk friendly area here. All the semi drivers at the elevator waiting for us, traffic on the highway stopped for us to cross, never anything but smiles and having our pictures taken.
I live in North Carolina, however, as an Army brat (then a transient adult), most state laws are similar.
Horses being ridden or driven are considered vehicles (as are bicyclists) and must obey all traffic laws...so are allowed an entire traffic lane. If you don't have turn signals, you must use hand signals when turning or changing lanes. You must stop at all stop signs, and follow the rules for rights-of-way.
Pedestrians must walk AGAINST the flow of traffic if there are no sidewalks.
Four years ago, my 21 year old nephew decided to walk home from work one night. He was walking on the same side as traffic, in a VERY well lit area by a school, and was struck by a truck and killed instantly. Initial determination? Driver NOT at fault, because pedestrian was walking with the flow of traffic. As far as I know, this case is still being fought in court.
Sad, sad fact, yet it is still a fact. Please know your local traffic and pedestrian laws, and obey them. It might save your family, loved ones or friends unneeded grief.
("Nos vemos otro lunes, tía..." I'll see you another Monday Alexis..)