They will just start making announcements, something like "The corrals are now open. All runners should now start proceeding to the corrals." And then 5 mins later "All runners should be heading to the corrals at this point." 5 mins later "Please, all runners to corrals now. If you haven't started, please begin walking over immediately." 5 mins after that "Last call for all runners to go to corrals." And then 5 mins later "Once again, last call, all runners to your corrals." And then 5 mins after "If you are not in your corrals, head there immediately. Last call runners." Followed by 20 mins of standing around in the corrals. These numbers may be off a bit for this race since there is no mile walk to the corrals, but the idea still holds.
People will both stand or sit, but the corrals aren't necessarily big enough for everyone to sit. I know at at least one of the races, I saw a corral that was spilling out into the area next to it as the corral wasn't big enough. Not sure if that many people up front were sitting and the people in the back just didn't move in, or if runDisney screwed up and made the corral too small. They will have a DJ playing, and sporadic attempts from the hosts to make conversation with runners and each other, and sometimes they show videos and such on the giant screens. Listen to the music, try to relax, and keep loose. If you are planning on running with a pace group (do they have them for the W&D?) look for the balloons, and chat up the pacer. Figure out their method and style. Don't be afraid to talk to other runners. It's usually pretty obvious if someone doesn't want to talk, but usually it's a great place to find out about other races you might want to do.
Don't bother with a foil blanket, pack a set of throwaway clothes (IE long sleeve and pants that you don't mind leaving behind in the start corral). Much easier to keep on you while moving/sitting, and runDisney will donate them to charity after the race. But odds are, you won't even need em. I'd be shocked if the temps at start are below 60, and wouldn't be terribly surprised if they were between 70 and 80.