Puck- unfortunately, Rainy has...issues with things on the ground. They actually seem to make her flip out even more. =P However, when she does flip out in the outdoor, there's nothing in there except the mounting block, which she's used to.
Ahsisi- Sounds like a plan, since two suggested it. Next time I ride out there, I'll try that out.
Ponies- I can't think of any wild animals, since the outdoor is pretty far from trails, the only spot where there would be animals; she's not afraid of dogs, either, since both of the B.O.'s have dogs that are almost always there. Umm, on side of the arena is the mares, one side is the manure pile/first barn, another is the other barn, and the last is a field. But her pasture is right next to the field, so she should be used to any sights/smells coming from there.