let it snow
This turned out much better than I expected; however, there are a few issues: 1. when viewed from certain angles a pattern is noticeable, but this can be fixed by using more than one snow texture and varying the texture alignment, and 2. the brushes move in unison. It would be nice to make one set of bushes begin their move while the other set is in the middle of its own. I don't think there is a way to time delay deformvertexes purely shader-side. It's not a super big deal as you have to sit still and really look to notice it.
After reflecting on what metl said about line of sight, I figure you probably don't want to fill massive open areas with rain/snow. But, I think if you correctly hint/optimize your map there shouldn't be an issue. Compared to particle rain/snow, this method is worlds apart in terms of performance.
Also, in the video the framerate dips because of the recording software, it's normally pegged at 1k.