I would say maybe even try a short little hack after a good training session for a cool down. Eventually you'll be able to leave for longer of periods of time and with less riding before hand to get the sillies out before they show up on the trail.
When I was still riding a bunch of greenies I kind of thought of a ride before the trail ride like longing a horse before getting on when they are really green and have lots more sillies in them.
If I was in your position I would really want to learn how to teach a horse to hack out nicely. You say they don't get turn out? So all arena work and no turn out may result in a burned out horse.
I'm not saying you can't think of enough ways to keep a horse interested and working in an arena, but now you would have one more way of working with the horse.
Change of scenery away from arenas is great for the horse and rider, you should really not give up and keep trying. Good luck.