I wonder how many people debating this have actually sat on a horse.
Leaving aside the frothings of BFF who clearly doesn't get most things, can anyone accept that riding a horse is totally different to any other form of transport that we are generally exposed to? The horse is fully capable of transporting himself, the rider's job is to select the destination, and to provide corrective inputs in case of problems. The level of interaction between rider and horse is many, many orders of magnitude greater than that between a driver and a car, or indeed a rider and a bike. To that extent, texting while hacking at walking speed, especially in pairs, is actually pretty safe, as the horse is following the side of the road, and his hacking partner, and the rider has a plethora of sensory inputs to tell him of what is happening. Some horses are easily spooked, others are solid as a rock. It's the rider's job to know their horse, and to act appropriately.
Mobile phone use while riding a horse is not against the law. It may not, however, always be sensible
Riding side by side is advised in certain situations, to prevent dodgy overtakes, much as with cycling. Whether it was appropriate to this instance, I cannot tell.