There seems to be plenty of detail in the hair, your zone III, so I think your metering is working technically as it should. That suggests to me that the 160 rating is just fine.
This is a place and fall issue. "Placing" the hair in Zone III is more likely the issue. I think the root problem here is that the hair and the face simply aren't 3 zones apart.
For any photo where a face is important I peg the face to the proper zone above all else.
The other possibility is that this has just been printed to dark.