I'm also heading there in January and hoping for nice weather. I went in Feb 2007 and it was rather chilly in the morning, but they had these big freestanding heaters out. Once the sun came out it warmed up a bit, and honestly if you just take the plunge in the water, you get used to it pretty quickly.
The park closes at 5 or 6, but there's enough to do from open to close. You go in to the reception building first and get your ID cards and assigned time for the dolphin swim, assuming that's the package your're doing. The times are first come first serve, I'm not sure if you can say "I'd like to do the swim around 2" or if its just "You were here first, you get the first time slot".
When we went, we got our welcome picture taken, then met an employee who gave us a very short kind of welcome introduction of the "Go to the left for the aviary and the right for dolphins, over there is where you get your wetsuit" variety. They serve a continental breakfast, but when we were there they had quiet a variety of food. You queue up to get your wetsuit and you have a few options here, a full suit, a "shorty" suit that ends at your knees and elbows, or a vest. They'll also give you a mesh bag to keep everything in. I believe they'll give you a locker key here as well. The lockers are free to use for the day. The bathrooms are large as they have shower stalls in them. They're really nice, and even have shampoo and whatnot in them to use.
If memory serves, you'll dolphin swim time will be printed on your ID card, as well as which pool you'll be at (there are 3).
We ended up leaving at 3:30 ish and had later ADRs which we had plenty of time to get to. I would have loved to stay the whole time, but the person I was with made things kind of hard (they didn't do the coral reef, the sting rays, or the lazy river so I felt guilty spending a lot of time in those attractions) I'd suggest making your ADRS a bit later if you think you'll be at DC for awhile if you're planning on eating, or try to go to an EMH PM park.
Hope that's the kind of info you were looking for (lol not the PITA I was with story but the rest of it)