We quickly decided that the Wemos D1 Mini was the way to go. With WiFi, lots of RAM and the capability to drive WS2812 directly, that's the perfect match for our project.
We then fiddled around with cloud-architecture. To quickly sum it up:
You'll need hot glue. Lots of it. Styrofoam is okay, but doesn't like hot glue at all. Cardboard works much better, and healthier too. Take care which batting you use, and preferrably buy local to be able to inspect beforehand. The best topology for the LED carrier is a torus, if you don't wan't to spend hours soldering LEDs together. It also looks very nice, even without the cloudy batting.
CloudyMcCloudface, Project Title "CloudIA", was born out of the idea of @Richard Deininger to build something like the Floating Cloud because that's a pretty cool thingy, but the price tag is just a tiny bit ludicrous.
So the levitating idea was ditched pretty early on, getting way too expensive with all the levitating and induction stuff going on, and we decided to possibly build something which just hangs from some ceiling.
What remained was the cloud. And because an "ambient LED lamp" is pretty lame to be honest, it was quickly decided that a weather forecast display was the way to go.