Absolutely, it’s horror… in fact it’s much more horror than typical campy outings the genre is plagued with (which have their place).
Drama and character building has a lot more impact when truly horrifying things, like the shocking ending of the mid-season finale of season 4 happen:
https://www.imdb.com/title/tt2948638/
I’m not going to spoil it. Horror isn’t just gore and death, true horror, is pain and loss, madness. Season 4 really delves into the madness of the character Brian (The Governor), probably the most fascinating and interesting part of the series so far.