Apollo and I have been on the road now for over six months. During this time, I've lost track of the number of people who have said they'd like to ride out with me for the day, but their horse wouldn't be safe to ride on the road. This is a smart situation in which to use such extra caution, because road riding is not at all like arena riding (although of course the same cues and lessons apply), and hardly like trail riding either from the horse's perspective.
But road riding is not an unattainable goal. Being able to ride safely around traffic, bicycles, dogs (not barn-saavy dogs), wheelchairs, four wheelers, motorcycles, and even semi-trucks is possible, and opens up so many more options for where you can ride your horse.
As a long rider, traveling along busy roads is unavoidable. Even the Unbranded team, whose goal was to ride only in wilderness from Mexico to Canada, had a few sections of road including a frontage road along an interstate. Apollo and I are at the other end of the route-spectrum: we avoid wilderness and stick to side roads where I can find them. But there have been plenty of times I've had to ride along state highways, and even along interstate 101 in Oregon.