"nature or nurture" is correct and usable in written English. You can use it when discussing the complicated debate around how much of a person's character is determined by environmental factors or by their innate nature. For example: Many psychologists debate whether a person's sense of morality is nature or nurture.
Nature or nurture?
Is pessimism nature or nurture?
Is it about nature or nurture?
Is it nature or nurture?
Dana Milbank - Nature or Nurture?
What is more important - nature or nurture?
Is this nature, or nurture, or what?
It's the age-old nature-or-nurture debate.
Few psychological scientists are still fighting the nature-or-nurture war.
It's in her nature -- or nurture: Her grandmother was a social worker, her grandfather a public schoolteacher.
On where the drive comes from nature or nurture: I would say half-and-half.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union