I don't do much in a round pen or arena. Most of my rides are on the mountain. Young horses get an hour at easy walk. 4-5 year olds will go out all day.
I keep my horses pretty well "Legged up" I don't tire them out so they are dead beat. But rather stay out long enough that they pay attention to me and stop fooling around.
My horses seem to enjoy a good trail ride. It gives them so many things to see and deal with. Corssing logs, streams, dark shadows, hikers, mountain bikers, pet dogs, birds like pheasants and turkeys exploding from cover, deer spoking and running off. It all helps the young horse learn to trust me. If they get a little excited, I can make them turn circles around a sagebrush until the calm down. If they really get excited, there is usually a steep hill close by to make them climb and burn off excess energy.
I agree you have to ride them in an arena or round pen long enough to fell comfortable that you can stop and control them prior to going on a trail ride.