Which is my horse's inside, anyway?

If you're used to thinking about the terms "inside" and "outside" relative to your position in the arena, you'll need to retrain yourself.

When dressage riders talk about inside and outside, they're referring to the concave and convex side of their horses. The concave side is the inside, and the convex side is the outside, regardless of where the center of the arena is.

Look at the diagram: for the horse who's bent left, his left side is his inside even if his left side is closer to the rail or wall.

There are many times when a horse's inside will be close to the rail: for instance, in any movement where the horse is counter bent (or bent opposite the direction he's turning), and also during many lateral movements.