Oh, I'm so glad I don't have SNOW to worry about. The frigid Texas cold is tough enough.
But I'm from Northern Indiana and I understand about snowballs. I agree that it shouldn't matter, long or short hair, they are still going to need a sweater or jacket outside. And you can always put a tee-shirt or jammies on her indoors if you feel she's cold.
Your post made me think of this picture. Enjoy, and only 3 more months until it starts to warm up for you.