Also, I prefer compasses with mirrors, which both are more accurate and also can be used to signal aircraft.
And always carry a rescue whistle!!! In the end, it's his whistle that saved his life. I bought this kind when I was a mountain rescue volunteer (it's required equipment). It has no ball to freeze up, and is so loud I have to cover my ears before blowing it: https://www.duluthtrading.com/storm-safety-whistle-57046.html