In certain contexts, "It's wet" can refer to the state of the ground after rain but, as a standalone statement about the weather, it would be taken to mean "It's raining".
As I discovered when I woke up this morning, everything was wet due to snow, not rain. Mostly because the snow was melting off faster than it was accumulating.
My point being context is needed to say it's rain for certain. I could say it's wet outside (there are even puddles), but it didn't rain. A few weeks ago we had extremely thick fog, to the point that everything was wet until the sun burnt off the fog.
Locally, we usually get more of our annual moisture from winter snow than seasonal rain.