I'll never be one to say you shouldn't worry.... While I think sometimes getting pushed past fears is the best thing for us, I'd never belittle a person for their fears. I'm a pro at worrying! I absolutely think arena work is good for you. I'm applying my interests to your situation and I shouldn't.
Just some stuff I feel more comfortable secured like riding bareback for balance, without stirups, different gaits, that kind of stuff. I like the freedom though of an open area. I know it probably sounds weird but I want to ride thru that road of trees. It's like a tunnel, I thought this weekend I would walk them thru. I don't see anything but the trees that could spook. It's fenced on both sides.
Besides some day you too WILL have an arena and maybe even a round pen:')