Well, I would not recommend anyone to go swimming or have a nice tea-party in the rain, but a few drops of water or a little snow doesn't do any damage Just make sure to ALWAYS clean and brush the fur after every outing! That'll keep it nice and fuzzy.
Side note: Only if the fur is "Air-brushed" water is reaaalllllly bad! (Air-brushed is something like special spray-paint)
Mine's all airbrushed. Tycho started out as a big white suit and all color was added. Since I've found it difficult to do anything less than two hours in-suit, I sweat & drink water pretty heavily, and I've run the suit through the wash machine once already. It didn't do any discernable damage to the airbrush work. All I did was turn it inside out, use a non-scented laundry soap without whiteners, and use the cold wash, gentle cycle. I then air-dried it in the sun on a rack.
I brushed it twice during the drying process and it looks like new. Water is probably less toxic to a suit than dried-on salty sweat & oil residue, I would think.