I don't write in the morning because I have a hard time functioning in the morning. My body likes to be asleep in morning more so than at night.
For my, the most productive writing time is 8pm to midnight. I can write during the day as well, but have a harder time not getting too distracted by the internet. I could close down the wireless connection but am not strong enough to do that. Like to have my internet available all the time.
The best time to write depends on the individual, but this works for me. Of course, if I get a job and have to work grave yard (which is possible) then that might change.
Today's picture book - The Princess' Purple Pants