Keith is right -- if you're talking to someone who will easily understand that you're talking about the weather, it's much more natural to just say something like, "It's really coming down now," without actually using the words "rain" or "snow." If you were talking to someone on the phone or on Skype or something, and you wanted to make it clear that you were telling them about the weather change, you could say something like "It's really starting to rain now" or "The snow is really coming down now." (There's nothing wrong with your sentences, though. They make perfect sense. They're just not what native speakers would normally say.)

'It's getting heavy now' or something would eb better, I think - without saying 'raining' or 'snowing'. :)