"How much does rain or snow affect ballistics?"
Without intending to sound like a smart aleck, I'd say it depends on how many rain drops or snowflakes any given bullet in flight hits, other weather factors (wind, temp, humidity), and bullet profile. The latter is obviously of great importance and is why pistol caliber rifles and blunt, round-nosed bullets like 30-30 and 35 Rem are popular woods or "brush" guns since bullets with those profiles purportedly display less trajectory deflection when hitting twigs, stems, etc.
Another consideration is how much distance exists between the droplet/flake impact(s) and the target.
All of that considered, there are some really cool slow-mo videos floating around in the vitrual aether showing bullets hitting droplets of liquid sustaining marked deformation upon impact. I'll see if I can track one down and link it.
Update:
This is a popular Werner Mehl / Kurzzeit video. Okay, the whole entire video is just pretty danged cool. But the video I was referring to starts at 1:59.
And while watching this I had a terrible college physics flashback. I recall there being like a whole chapter on trajectory. Other factors I didn't previously mention would be (and this isn't in any order of importance): velocity of both the bullet and the drop/flake, density surely comes into play (likely a constant with rain drops, but with snow?), size of drops/flakes (skier's flakes vs. snowballer's flakes), and the individual trajectories of both the bullet and drop/flake prior to collision. And where on the bullet the drop/flake collides with it (nose vs side or tail of the bullet)
There's probably other factors- we have any physics gurus that want to lecture more about this (since all physicists love to lecture...)?
One final remark...sorry, but I just can't keep quiet at this point. Despite the video being B&W, the liquid seen on the video at the 1:59 time-mark is opaque and can be assumed to be something other than pure water (or water approximating the density of rainwater)- so we don't know its density. Incidentally, it looks like paint. And we don't know the composition of those bullets (plated vs jacketed, alloy composition, etc) or the other aforementioned variables. All you can say is that the impact between that particular liquid droplet and bullet caused deformation. If it was a rain drop, it could possibly cause less deformation or maybe even none at all. The implication in either case being that the droplet impact and any subsequent deformation cause a deviation from the intended trajectory of the bullet.
Incidentally, I have no practical knowledge of any of this. I tend to remain inside when it rains/snows.