The Shulhan Aruch (Orah Haim 4) brings an opinion that the morning hand washing must be performed specifically after the point of Alot Ha’shahar (daybreak, when the first rays of light appear on the eastern horizon), as it is at this point when the Tum’a (impurity) descends upon the hands. We do not follow this opinion, and thus one who rises before Alot Ha’shahar washes his hands when he wakes up, with a Beracha. Nevertheless, the Shulhan Aruch writes that if a person wakes up before Alot Ha’shahar, he should try to repeat the washing after Alot Ha’shahar, though without reciting a Beracha.
This is very common, particularly in the wintertime, when the sun rises later, and also during the month of Elul, when people awaken before sunrise for the Selihot prayers. One who awakens before Alot Ha’shahar should try to remember to wash Netilat Yadayim a second time after Alot Ha’shahar, though without reciting a Beracha. This Halacha is mentioned by Hacham David Yosef (contemporary), in his Halacha Berura, and also by Hacham Baruch Ben-Haim (1921-2005), in Torat Baruch.
Summary: If one wakes up before Alot Ha’shahar (daybreak), which often happens in the wintertime, and during the month of Elul – then he washes his hands with a Beracha when he wakes up, but he should preferably repeat the washing without a Beracha after Alot Ha’shahar.