If was offered one of two options for winter - all-wheel-drive with all-season tyres, or front-wheel-drive with winter tyres, I'd take the front-wheel drive/winter tyre option every time, and if you live somewhere where it gets cold and frosty in the winter, you should too.
I say this every year, and every year I get emails and pushback from people who think they're a waste of money though. The simple matter is that once the temperature of the road surface drops below 45F / 7C, your standard "all season" tyres are really not very good. Most people will think they're just fine, but trust me - once you drive on winter tyres just once in poor conditions, you'll gain an appreciation for what a compromise all-season tyres are. (Summer and performance tyres are even worse).
It's all down to the rubber compound and the tread design. In snowy weather, the sipes in the tread allow for much greater 'grip' on snow. This doesn't mean you can drive like you do in the summer - it doesn't make you invincible - but it will certainly making turning and stopping much more predictable.
For non-snowy climates, the different rubber compound is the benefit - it is much more flexible at colder temperatures meaning better ability to flex and deform to the normal road surface, offering more chance for grip.
Summer tyres are designed to work in much warmer temperatures and the rubber gets fairly inflexible and stiff once it gets cold.
All-season tyres truly are a compromise. They're not very good summer tyres and they're not very good winter tyres. They're designed to be a jack of all trades but a master of none which is why they're standard fit on most cars.
If you do decide to go for winter rubber, there's two things to watch out for. First, if you have winter tyres and the person behind you doesn't, you WILL be able to stop on snow and slick roads much more quickly than they can, so bear that in mind.
Second, there's two ways to do the summer/winter switch. Either have the tyres swapped on and off your rims twice a year, or have a winter set of wheels with the winter tyres permanently mounted. If you do that, make sure the winter wheels have the relevant TPMS pressure monitors in them or you'll spend all winter driving around with a warning light on the dash telling you there's a TPMS error.