All terrain tires work as well if not sometimes better than winter tires. I have a Ford F-350 that I drive in the winter with Bridgestone Dueller APT 3's. I am living in Alaska, of all places, and I have never had problems driving in the winter on these tires. If you want to buy all-terrain tires, make sure the tread is such that the snow can easily escape out to the sides rather than to the rear so the back tires aren't dealing with the same snow and it's not building up on the tire creating slicks.
If you're very worried about the snow and you WANT snow tires, be aware that there are two types out there: Studded and non-studded. Studded tires have studs of metal that bite into the ice, decrease your fuel economy, and have to be taken off after a certain date every year. Studless snow tires (like the Bridgestone Blizzaks) come in even load range E for the big trucks. They are made of a softer composite rubber so they stay soft and pliable in colder temperatures. In a 2007 study done by the University of Alaska, the Blizzaks studdless snowtire out-performed studded tires when stopping on ice.
My honest opinion is that if you drive smart - slower than the speed limit, slow around corners, brake sooner for red lights, and keep a larger distance between yourself and the car in front of you - you would do just as well with those all terrain tires. If you want a little extra security, put sand bags in the bed directly over the rear axle before the first snow flies and let those bags freeze in place for added stability.
Hope this helps. Good luck this winter!
Source(s):
Lots of personal experience: grew up in northern lower-Michigan and then moved to Alaska, so lots of experience driving in snow. Also I worked for Sears Auto Center where we not only recommended, but also sold and did the actual change-over of tires.