Yes, they are slightly different in nuance. It's snowing means that it is currently snowing, i.e. it is ongoing. It's snowy can be an indication of the fact that there is snow outside in general, and doesn't mean that snow is falling in that moment. Thus, it's best to use it's snowing when snow is actually falling, and it's snowy to indicate that snow is on the ground outside but not necessarily snowing at that moment in time.
Ex: I hate commuting when it's snowy. Traffic gets bad and it's dangerous to drive.
Ex: It's so snowy outside, let's go sledding!