I've started all my horses with riding on a trail. That way the question of where to go is obvious, and I'm just a passenger.
However, even when they're going really well with this, and I"ve moved from being just a passenger to suggesting and rewarding things like turn down this path instead of that, and stop here, not there, and lets go now, they still get confounded by the "goingnowhereness" of the arena, when it comes time to polish up their skills in the arena environment.
In the past I've used the "tap on the butt" cue for forward movement, and R+ for steps in a straight line. Sometimes really hard to get!
This time with Miro, and to a lesser extent with H, I've made it even more R+ only, and used target stations instead to ease the transition. Targets set up in the four corners of the arena. Reward each time we get to one, regardless of the time it takes or the wonkiness of the path (best if taught from the ground first, then transferred to ridden). We stop at a target station and reward with somewhere between 1 and ten "touch the target" repetitions, before I quit the reinforcement, and cue to move on to the next station. Once they're confidently striding out in a beeline for the target I point them at, then I start missing the odd target, ie, ask them to continue without opportunity to touch it, on to the next station and reward for a while there. Then we can do whole circuits, and add in transitions etc, and when I think the time is right, stop at a station for some intensely rewarding stuff.
It's worked really well.
I have not sought the horse of bits, bridles, saddles and shackles,
But the horse of the wind, the horse of freedom, the horse of the dream. [Robert Vavra]