Let's not get too carried away here!
Horse travel has been around far longer than motor vehicles and I suspect that there would be many who would say they have right of way (much like sail having priority over motor in the boating world).
If horses are banned due to them '..not being suitable to todays road conditions..', how long before someone decides that m/cycles should also be banned due to the high percentage of motorcyclists who are injured/killed on the roads each year?
IMHO if you're riding around small country lanes you should expect to find horses, tractors, mud, diesel, etc. since that's the norm. (whether you think it's right or not!). You don't often see a horse rider travelling down a dual carriageway as this tends to be the natural domain of the motor vehicle.
When in the countryside you have to be prepared for countryside hazards, just like in town you have to be ready for the hazards there (cameras (!), pedestrians, etc.). You have to adapt your riding to the environment you're in. There will always be the minority in a group who will upset it for the rest as Antony says - but mostly I've not had a problem with horse riders.
I don't know if a horse rider needs any training and/or insurance before venturing on the road (I suspect not), perhaps CK can comment on this - I feel sure she'll want to
