She looks to be at least part Thoroughbred. She looks like a lovely mount. The tie down, I wonder why that is necessary. It looks like the type used in barrel racing. It looks tight enough that it isn't allowing her much freedom of movement; she will always feel it contacting her nose in almost any gait she does. And, it is not connected to the breast strap, and I think it should be.
I am not familiar with such tie downs. I have never used one, and my first impulse would be for you to consider removing it, unless you know for sure she has a bad habit of throwing her head up and might break your nose.