Definitely dress in layers. We usually keep a blanket plus some hoodies for each kid under the stroller. They wear them in the morning when they first head out to the parks, take them off as it warms up, and then put them back on after the sun goes down. Now, with two teeny ones, you may not actually be in the park that whole time, but it's nice to have that as an option. The weather's a bit unpredictable, so I'd check a bit closer to when you're going. Like a previous poster said, you may end up with shorts and t-shirt weather!
Definitely also try to bring a change of clothing for each kid in case of accidents - we try to do knit pants/leggings and light long sleeve shorts for both pairs of clothing so it's easier to roll up and stick in the stroller. For diaper/clothing changes, I have a small toddler-sized backpack that I keep all the diapers, wipes, and clothing changes in, and I clip that to the stroller with a carabiner - makes life much easier to just grab that and go rather than rummaging around in the stroller for everything if there's been an accident!
If it's really cold and you just need to warm up, there's the animation building at DCA and the Star Wars Launch Bay at DL - you can't bring the stroller in to either place but the kids can run around inside. They also might like the Disney Junior Dance Party (or whatever it's called now) in DCA, which is inside.
I'm guessing it'll be more than just you and the two kids, so you can use child swap if you want to ride anything the kids are too small for. Basically, you bring your whole party up to the line entrance and ask the CM for a child swap pass, telling them Adult 1 will go on the ride, while Adult 2 waits with the kids. They'll scan Adult 2's ticket and give them what's basically a FP that starts at the approximate time you'll be getting off the ride and lasts for an hour. When you're done riding, Adult 2 can then ride using the FP line. When my kids were little, my husband would get an FP for, say, Space Mountain, and I'd grab one for Big Thunder Railroad during the kids' nap times, and then use child swap so we'd both get to ride both rides. If your kids will sleep in the stroller, this can be a nice way of getting some grownup time. We still have fond memories of pushing our sleeping kids around the park and just enjoying the sights.
But I know it gets chilly in the evening. I will wait till we get closer for clothes planning.. (we are going the same days too!)
