I don't think you can parent 2 things to the head. So that's probably why one set of horns isn't working for you. Just like you can't parent 2 objects to one hand.

If you put the horns on the head then go to Figure / Set parent and picked the figure's head, the horns will stay on.  The others I think you will have to manipulate into position for each render and just  leave them unparented.

"It is good to see ourselves as others see us. Try as we may, we are never
able to know ourselves fully as we are, especially the evil side of us.
This we can do only if we are not angry with our critics but will take in good
heart whatever they might have to say." - Ghandi