Небеса станут серыми or Небо станет серым. The English "to turn" here means "to get, to became" and this is Russian "стать". Or you may use the verb "посереть" - "to get/became gray" Небеса посереют, небо посереет.
"Обратиться" in this sence may be used in cases like "He turned a wolf" "Он обратился волком", otherwise it is "to address, to apply".

As for the difference in meaning, Небеса is indeed more often the place where angels live rather than simply "blue sky", but Небо is both, I think. The word is a word as such, with all its meanings, and all they may become important, especially in poetry. There is no one-to-one correspondence not only between the words but also between the conceptions (world view) in different languages. That's what makes them interesting to study.