You shouldn't consider for a second an all season tire to use only in the winter.
First off, there are plenty of performance winter tires. Winter tires are designed to work when it's cold, all seasons are designed to work in any temperature range. When it's cold, the compound for the winter tire is just better in all ways. Not just when it snows. Not all winter tires are snow tires.
Second, winter tires last just as long as all season tires. In fact, all season tires wear poorly when it gets cold, especially high performance all season tires. You will probably get twice the mileage out of the LM-60's vs the DWS's just to pick the two mentioned in this thread. The reason winter tires are replaced more frequently is because tires intended to be driven in the show should be replaced at 6/32". All seasons are often replaced at 3/32". They'll suck in the snow but people keep them far longer. For winter use, an all season tire at 3/32" when you expect occasional snow is NOT GOOD!
Third, lets talk about how much all seasons suck. They're basically made for a huge temperature range and have varying degrees of ambivalence towards snow. Something like the DWS's linked here which is an UHP AS tire are terrible when it gets cold let alone snow. The compounds are made to be decent when it's warm and even designed with occasional and brief race-type use in mind. That means they deal with heat. There are no rubber compounds on earth that deal decently with heat that don't turn into hockey pucks below freezing.
Buy some cold weather tires. Don't think of them as winter tires. Buy tires that are good when it's cold. Since you don't need to run them in the summer, an all season would be a poor choice. Leverage the summer set you already have by buying a tire to use only when it's not hot.
2015 STi: Still Stock
04 STi, 04 WRX: SOLD