I don't know about RF3, but I think that's pretty normal for the Bokumono series at least. I know in Trio of Towns you can see little sprinkles of snow starting in late fall, at least in Westown (not sure if you also see it in Tsuyukusa or not, but you definitely don't in Lulukoko). I think they're just mimicking real life. We *always* have snow long before winter is technically here on December 21, where I live...permanent snow usually sets in around mid-fall, here, sometime in November.
Basically just like Kikki said. It’s a nod to real life and it doesn’t effect your crops or anything. Once Winter 1st hits, they’ll be a lot more snow.
Don’t recall if it happens in 3 but in some games, towards the end of Winter, you’ll start seeing patches of green.