Depends on if you want to drive safely in a snow storm, or just rely on hopes and prayers.

EDIT: AWD only helps you accelerate, which is arguably the least important main function of a car. AWD does effectively nothing to improve turning or stopping. This is where snow tires come in. They have significantly more lateral grip, and drastically reduce stopping distances in snow/ice conditions.

If you can change your schedule to not drive in the storms, you'll probably be okay with all-seasons. But if you have a job or other commitments than require you to be somewhere no matter what, snow tires are the right answer.