Definitely. Horses don't generalise well & are very aware of particular details, circumstances & environments, so it's common for them to behave differently in different environments. For eg. A lot of horses are trained & ridden almost solely in arenas, and when they are taken out into the wide open, they blow a fuse, because they're neither trained in that environment, or comfortable & confident in it.
It sounds to me as if your horse was trained rather forcefully/mechanically to perform in the arena. That he goes into automatic, robotic kind of mode when in there. That he wasn't taught to be comfortable, relaxed, confident in this environment. If you want to change this, get him left-brained & thinking, not just reacting to his 'programming', I'd be inclined to just go there & hang out with him, feed him, groom, walk around with him, etc. Once he's confident & relaxed just being there, then you can try same sorts of things when you're aboard.