Practical Examples Of Metlslime's Idea
Although none are actually weather effects, the following models demonstrate the idea of creating particle style effects which disappear and then reappear to allow looping in engines with interpolation:
forcefield and smoke. The forcefield is the closest to the idea as the particles loop - even though there are particles going in both directions, if you track any one you'll notice that it only ever travels in one direction. The smoke is actually performing a similar trick, but because it's a big long thing it's harder to spot.
runic barrier. This is also similar to the smoke, but because it's got a greater number of distinct "particles" it might be more representative.
embers. These aren't intended to loop as such, but they demonstrate the idea of particles disappearing into nothing. They also exhibit a nice "floatiness" which might be good inspiration for snow.