You definitely take the entire day there... especially with the cost of entry! Are you only in the area for the day? Because when you buy a DC ticket, at least when we were there last, you also get a 5-day pass to Seaworld included...
Anyway, it is a full day. We went the first week of December 2 years ago and had no problem with the weather. I'm sure it won't be pleasant in the cooler months if it's raining, but aside from that I think it would be fine. As I recall the fishless winding river is heated anyway, isn't it? The tropical fish and dolphin water are ALWAYS cold for the fish - if anything the water may feel warmer because you aren't going from HOT air to COLD water. And as someone stated above, you can opt for a wetsuit versus just the lifejacket.
But between ray feedings, bird feeding, lolling down the lazy river and checking out the tropical fish, the day will fly by before you know it. And it's a great break from all the walking you do at the other parks. It's the only park my anti-Disney dad will go to.