Another note on personal experience --
I had a set of BFG mud-snow tires, similar to the AT, but heavier snow tread.
I just installed them on stock rims and when the season got 'snowy', put them on for a few months. Very aggressive tread, but great in the snow. Wears out much quicker, but it's only seasonal, so lasts a while.
Nothing does any good in ice - except spikes or chains - but these were the next best thing.
Extra set of seasonal tires is handy, much better than messing around each time the weather throws a punch.