there should be closed bike carriers like they have for skis.
on a separate but related note
I washed the salt off my bike on a day that was almost 50 degrees and then when I rode it on a day in the teens the rear der cable was frozen to the rear der cable housing. I had to do a nightime roadside field repair in the snow. it took a good 15 minutes to free it up and get it adjusted right. not amused.