I'd say it really boils down to one's definition of "fun." If you find the thought of riding in a driving rain storm, or on roads with icy spots and bitter cold, to be a "fun adventure," then yes, it probably is POSSIBLE, though may not be advisable.
For probably 99 percent of scooter riders, it's not even a consideration. I was just telling my son last weekend that as far as I am concerned, anyone in Pennsylvania who has a two-wheeled vehicle has a luxury, because on rainy days, windy days, winter, etc., it's basically not practical.
Again, if you are in the elite 1 percent, more power to you. But none of that sounds the least bit enjoyable to me.