Dream fastpasses, Dream Lanyards & Pins, and Dream Ears appear to be handed out for the most part between 9:30AM and Noon. After Noon you typically don't see these prizes get handed out.
I would also say that castle winners appear to win between 10:30 and Noon each day. Since the winners have to be in the 3:00PM parade there needs to be enough time for the winners to go back to the hotel, get an overnight bag together, make other arrangements if necessary, and return to the MK before the 3:00PM parade starts.
Other dreams..probably larger prizes.. can happen anytime during the day. I've never seen or heard of a large prize getting handed out after 5:00PM. Some people have reported winning an extra hour after close in a specific park after 4:00PM.
Hope that helps and good luck.