I'm currently playing Curse of Strahd. Personally knowing some actual Vampiric Lore and having also read through the Monster Manual, I know that running water is a weakness to Vampires.
Is rain considered Running Water for a Vampire's weakness Harmed by moving water?
This was brought up, in our game, due to Strahd standing out in the rain for our first time meeting him.
It isn't really well defined.
In most mythology/settings, rain doesn't count as running water, and to a lesser degree, neither do lakes and oceans.
Rivers and streams definitely count, but anything beyond that is up the game master.
Personally, I would not include rain, as it would make it impossible to have a cool battle in the driving rain on a stormy, moonless night.
When people say "running water" with no context beyond that, it invokes images of rivers and streams. Maybe a water slide. Possibly a sink faucet. But very few people are going to think of rain. "Running water" here is meant to imply natural sources of permanent water that moves. Rain or emptying your waterskin on Strahd and claiming the water was "running" when it contacted him goes against what vampires are supposed to be vulnerable to.
Also, I am about 97% certain Strahd is depicted somewhere throughout the book as standing on the ledge of a cliff or perhaps on a balcony while a thunderstorm rages on. This seems to put a nail in the coffin (see what I did there) of any notion that rain should count as running water, as Strahd voluntarily stands in it on occasion.
