Can I do the snow/rain effects in GIMP? And if so how?

SNOW
Works for both Photoshop and GIMP.

Create a new layer
Switch to brush tool with a diameter slightly larger than your desired snow size. Move at random and click. Make sure that you are NOT moving when you click (ie draw a line). You want circles.
Copy that layer
On the copied layer, do a Gassuian blur at about 2-5 px rad. This layer is now done.
Go to the original layer and erase a couple of the dots, BUT NOT A LOT. It doesn't matter which ones, just find a few and erase the entire circle.
Use the magic wand or fuzzy select to select a few of the circles. Try to not follow a pattern.
cut the selections to a new layer
For each of the two layers, select motion blur and set the angle and stretch length to a level you like.
Adjust the fade of the two streaked layers to make them decently translucent
Slightly lower the transparency of the first layer mentioned earlier. It should not be less that the other two motion layers.

And I have no clue on how to distort with rain.

Rain is the slanted lines, same concept, just without the blurrs~