No, Watership Down is full of disturbing events. It's a great book, but not cozy.
The Girl With All the Gifts was cozy for me, but in a "death is beautiful" kind of way, like the story of Hel, for example. It's a zombie apocalypse in which the child zombies are mysteriously sentient, but still crave living flesh and will attack uninfected humans. The bulk of the book is action scenes along the road to solving the mystery of why. It's not what I would typically think to recommend as cozy to someone, but I can't recall any especially intense scenes.