I also have won all my prizes early in the morning, except the 2008 Dream Magic Hour at Epcot, that was early afternoonish.
I think its easier to win prizes in the morning because there are less people in the parks. The less people you are competing with, the higher chances that you'll win the prize. It makes sense statistically, if there are 500 people in the park, and they are giving out 100 fastpasses, you are more likely to win than if there are 10,000 people in the park and 100 fastpasses.
I have also won the most at Epcot, and I think that is also due to statistics. In the morning there are less rides open at Epcot than at, say MK, so if they are going to give out dream fastpasses between 9 and 10 am, there are less venues to distribute them (i.e. WS is not open, nor is Ellen's energy adventure), so your chances of happening to be in the right place at the right time are increased.
If you are looking to win, here is my friendly insider tip, ride Soarin' over and over again between 9 and 10 am. I have won dream fastpasses on Soarin' 3 times between the hours of 9 and 10 am. I know, I'm lucky!