The flame effect is missing a couple of things, which I may get time to add later: it needs a glow effect (ideally one which has lit rain on it when its raining to give the impression the fire is lighting the rain drops), it needs a distortion effect, and also smoke.
Here's what I've got so far for the rain. You'll notice I'm also reducing the direct light whenever its overcast. The sharp shadows during rain obviously weren't right, but this introduced the problem of a darker scene, so I decided to use postprocessing to compensate. I also introduce more fog during rain.
I experimented with a ring around the player with rain falling on it, but I abandoned this in the end because it was too obvious that the rain moved with the player whenever the player strafed. It occurs to me now that I may be able to scroll the texture with the player strafing, but this may prove fiddly so I'll leave it for now.
I tried out a really quick lightning system which basically just enables a light very briefly intermittently during a storm. This looks okay, though it is noticably absent in lighting up the sky at this time.
The snow particles drift down in a natural-looking manner, which I'm fairly pleased with. I would have liked to have gone for a stronger blizzard, but this would have required me fixing up something clever with the precipitation ring mentioned above, and/or using a lot, lot more particles, which I'm reluctant to do given the strain my level is already putting on the performance.