I wouldn't recommend taking the risk! All-season tires do work in winter, but the grip quality drops noticeably, especially when it gets below freezing. The rubber becomes stiffer, and the tread doesn't handle ice and snow as effectively anymore. Sure, technically you can drive on them, but your braking distance will increase, and in a critical situation that could make a difference.
The main thing - there's a hidden catch that people often overlook: all-season tires wear out faster if you drive on them year-round in harsh conditions. Winter wear plus summer wear means the tires won't last as long. So you might save money on not replacing them, but then you'll end up overpaying when you have to buy new sets sooner than expected. Plus, if you get into an accident on all-seasons on black ice, your insurance might have questions!
If you really want to save money, it's better to spend once on a proper winter set. A lot of people buy cheaper tires or grab them on sale, store them in the garage for six months, then just swap them out. Yeah, it's a hassle, but it's safer and more cost-effective in the long run!