Sahih Muslim Book 7, Hadith Number 2964.

Chapter : It is excellent that the aged and the weak, especially among the women, should hasten from Muzdalifa to Mina at the latter part of the night before the people moving in multitude. and excellence of staying there for others until they observe the dawn prayer at Muzdalifa.

It is narrated from Umm Habiba: We used to set forth from Muzdalifa to Mina, (very early in the dawn) when it was dark. And in the narration of Naqid (the words are): “We set from Muzdalifa in the darkness (of the dawn).”