The recent snow storm got me thinking about this. So are you allowed to eat snow? What about icicles?
I wish that I could locate a definitive source to answer your question, but, in a way, the answer seems a rather obvious "yes it is kosher. My deduction:
Almost all drinking water occurs "naturally". If you or anyone else has hiked into a forest or anywhere that has a spring, esp. in the beginning of the Spring season, that water originated from snow that melted and seeped into the ground or flowed into a stream or river. Along the way, who knows what else may have gone into that stream - traces of animal feces, microorganisms (amoeba, hydra, etc.), perhaps traces of non-kosher pork chops from a camper's barbecue next to a stream somewhere. People either drink from the stream directly, or if buying bottled water, they're drinking that.
If you're wondering why does bottled water have a heksher, I asked someone from the OU a while ago and he explained that it has to do with the processing plant which may process other non-kosher products in the same plant. But spring water itself needs no heksher.
If you drink tap water, there's no heksher on that. (Yes, I know that there have been attempts to get one on NYC tap water, but so far, those efforts failed.)
I'm trying to make a "kal vachomer" in a way. If you're essentially drinking melted snow without a heksher, I think that whole unmelted snow doesn't need one. Granted, I don't recommend eating "dirty" snow from the street and certainly not from the road. Personally, the concern with such dirty snow is not its heksher but far worse - I don't recommend drinking a slush mix of gasoline and calcium chloride.