One more thing, if you're looking at it from cost perspective, that makes no sense either. If you get winters or all seasons, you're really signing up for the additional cost of the wheels themselves. As someone already pointed out, you will be using each set half of of the year, so the overall cost of use it still the same. You still eating the same amount of tire per wheel revolution. The difference is, you're buying an extra set of wheels to mount them on and you're fronting more cost upfront. But, it's really not THAT much different in the end.
Cost of A/S tires is comparable to winters. So, why would you spend the same money for a inferior product? Unless you're really looking to have just 1 set of wheels and tires, there is no reason to run all seasons in winter. None. A/S tire, jack of all trades, master of none.