I really don't. I don't sleep long, and when I'm asleep, I stay asleep unless my brain sounds an alarm (I've been instantly awakened by strange noises or the like, but when it checks out, I go right back to sleep). When I do wake up, I'm refreshed, but I don't generally bring my dreams with me. However, morning is my most creative time, so in a sense I suppose I do night write. My mind processes things overnight, but I don't have to scramble in the dark. It's all there when I begin my day.
I prefer to night write as well. It's the same feeling I get when I watch a movie in the day as opposed to at night. At night it just feels right, bears more weight and importance.
I night write because I have a day job . Well, I sneak in twenty to thirty minutes before work in the mornings, if that counts. If it works for you, then the world is yours.
I just like writing when I'm feeling a little sleepy. Being tired slows my thoughts down just enough to let me stay focused. I've been able to get a similar effect from some light meditation, so I would suggest to anyone who has trouble writing because of distractions or scattered thoughts to try meditating a little. Just sit down, or lay down, relax, and focus on just one topic to think about. If you're afraid you will forget the ideas that come to you, take some notes right afterwards.