Thanks for the replies!
I guess I was confused because in the training plan (NF of Eiger) it mentions that hill hikes can be substituted, but to add weight in the Zone 2 run descriptions. But it makes sense to not add weight to ensure that you are building your base correctly.
I agree with Aaron, that pretty much any running up hills for me at this point is pushing into Zone 3. I think I will go with the hiking the hills and running flats and downhills (I essentially do this when trail running for the most part anyway).