Like the skin hurts? Or the inside of your nasal passages get dry? If the skin hurts, and if your skin gets chapped around your mouth and nose, I find that it helps a lot to put a thin layer of petroleum jelly (Vaseline) on before heading out. This also helps keep you warm on any skin you have to leave exposed when it's *really* cold out.
If your nasal passages get dry, you could try saline nasal spray, and my sister raves about this ointment called Ayr saline nasal gel. Not sure if that helps.