Usually I just stuff it under a baseball cap at the stables.
My hair is pretty long, and I do the same thing as you, put in ponytail and put on a ball cap.
I was doing the computer work for the Bloomfield Open Hunt dressage show (once a major national event), and was picking up completed tests from one of the rings. Passing by some stables, I noticed what looked like a chip of red barn-wood in a dried-up tire rut. Except I got curious, because the barns there were all white, and not red.
I kicked at it, and it wasn't a chip of wood at all, but a really-trashed Swiss Army knife
It was as jammed up as if it had been filled with concrete. Mud had seeped in, an gotten hard as stone. After six months of soaking, blasting in an ultrasonic cleaner, more soaking, and digging with a dental pick, I got this
Everything works, even though it's a bit rough. The Wenger shield got popped off long ago as it sat in that muddy rut, being driven over by trucks and horse trailers. I have no idea how many hundreds or thousands of people passed by it, without thinking to take a closer look.
I've tried wearing ballcaps, but I think I've got a funny shaped head and just look awful in them. I like my visor.
Becky