I have to say, that that is the first I have ever heard of anyone leaving a hrose in a rope halter out to pasture. It is just way too easy for what you saw to happen, and they DON"T break, and they are harder on the skin. You got super lucky you didn'thave a worse result, and I appreciate your courage in sharing that mishap here, so that no one else will make the same mistake.
So glad your mare is ok.
I second a breakaway halter (has a leather crown piece that can break in a panic, and is replaceable), if you must have something on the hrose to catch them.