No surprise there - the "living like nature" part was the whole schtick of Nietzsche's philosophy. More like an Epicurean with a healthy dose of Cynicism than a Stoic, if we have to make that kind of basic comparison. He would probably conflate Stoicism with the (nowadays prevalent and in many ways successful) "English" approach to values, which he considered a reversal of the "true" values that's driven by resentment, and a philosophical dead-end.
Though Nietzsche did also develop a highly refined statement of "living in accordance with unchangeable nature" through his idea of Amor fati. The fact that he acknowledged this principle so thoroughly despite opposing many other parts of Stoicism must surely be of some significance.
>Though Nietzsche did also develop a highly refined statement of "living in accordance with unchangeable nature" through his idea of Amor fati.
He looked down on any philosophical idea that uplifts your soul like stoicism, buddhism (deliberately making his work and ideas seem scary to them: happened to me when I first got into his ideas) etc
He discouraged philosophical frameworks because he believed that in the end they limit human life. A truly well lived life, according to Nietzsche, is one where the individual breaks free of indoctrination and dogma, and lives life as they want. In the truest sense. This is Nietzsche's goal for humanity, so he spends his time writing philosophy aimed at tearing down religion and systems of moral control. Nietzsche wants to free humanity...
Though Nietzsche did also develop a highly refined statement of "living in accordance with unchangeable nature" through his idea of Amor fati. The fact that he acknowledged this principle so thoroughly despite opposing many other parts of Stoicism must surely be of some significance.