Allay thy fears and quail not. The things don't melt. You can fly them in downpours (not especially recommended, but you can do it).
The biggest issues are:
- The lens: Water on a lens makes for an interesting image but not typically one that your were planning on. It just takes ONE drop of water to mess up an image. The water tends to evaporate / fall off, but ofttimes his little buddies come looking for him.
- The camera / gimbal: Can be damaged by longer term water exposure. I had a P3P lost in the woods in SE Alaska over a winter. The gimbal sort of worked (after some WD40) but eventually had to be replaced). But it sat out in 1 inch per day rain for several months. But brief rain probably won't harm it. If you are anywhere near an ocean, the dissolved salt in rainwater CAN cause problems later on so it is an excellent idea to wipe down your electronics after use. And never store anything wet.
- Batteries: Really shouldn't be submerged or soaked (duh).
But flying briefly through rain won't hurt anything as long as you dry it off carefully.
Some other things to consider - water is an excellent absorber of 2.4 GHz microwave energy (and 5 GHz as well). Expect problems with the radio link in precipitating environments. That includes the GPS reception (as any boater will tell you). That can be a problem. I think my aforementioned loss of the P3P was due to flying it in a snowstorm, losing GPS and having it wander 'home' a few miles away from where it was supposed to be. If I ever pull that sort of stunt (it was a pretty scene), I think I will set it up so that loss of signal just causes the AC to hover / land instead of trying to muscle it's way through a blizzard.
I tend to avoid flying in storms because there isn't much utility in it, but I will go through squalls, rain showers and fly near precipitation.
I don't think DJI has a moisture sensor in any of it's products, but that is something that has frustrated some cell phone users ("No, I didn't drop it in the toilet, why would you think that?").