This has been an issue since 1.14 launched; weather comes through blocks as though they aren't there. This wasn't a problem at first, although having it rain inside my underground room (beneath two more floors of my house) was pretty strange, but when I moved into a mountain, and snow began coming through layers of 'solid' rock, it started to get really annoying. I have had to disable weather entirely.
This may be an issue that only affects pre-1.14 worlds- the world where this bug occurred was created on 1.8- but I haven't tested it yet. Hopefully this gets fixed in 1.15 or 1.14.6.
Did you open the world in any 1.14 snapshot?