i'd like to echo what custardpsc said. As far as the rain goes - it depends where it's coming from - if you have patchy showers coming from small cumulus clouds, generally you can see through it and its fine. If however you are looking at warm fronts/nimbostratus clouds, you're looking for trouble, the visibility will not be uniform, you can enter the rainy bit and still see for a while, but the vis can drop rapidly and you can end up in a cloud in no time. Generally use common sense - if you see what's behind the shower - its fine, if you don't - don't go in it!
Snow wise it's the same story, however with an added risk- rain generally falls vertically down and as you fly through it you will notice the droplets going downwards and towards you which will feel natural. Snow however, if the flakes are light can go sideways depending on the wind. This can cause illusion that you are turning
Icing wise - unless it is really really cold, you will get air frame and prop icing sooner or later. They say that in order for the ice to not form you need to be in below -40'C, so yes - falling snow is icing conditions, don't go in it