Successful handling of an automobile on snow and ice depends on two factors: skill and equipment. All the previous writeups in this node have emphasized the first. But no matter how good a driver you are, your car's performance on frozen surfaces will be far from optimal if its tires aren't designed for the task.
Simply put, if you plan on doing any serious driving on snow, you need to get yourself some snow tires. If you live in an urban area and the only winter driving you do occurs on flat, city streets which are quicky plowed and cleared when snow falls, you might be able to get by with the driving techniques described above. Even then, though, a sudden blizzard could easily leave you in a ditch. But if you'll be driving during the snowy season on highways, steep inclines, irregularly plowed country roads, or even (especially!) roads where snow melts and re-freezes into ice, a set of snow tires is a must.
Sure, all that's been said about steering out of skids is important. But wouldn't it be better to avoid skidding in the first place? A four-wheel drive vehicle will help you drive through heavy snow, but as many SUV owners can attest, four wheel drive doesn't mean four wheel stop. And antilock brakes won't do you much good if your tires won't grip the surface you're trying to stop on. Snow tires, unlike "all-season" tires, are built specifically for these conditions, and I can tell you from personal experience that they're far more effective than anything else except snow chains, which are immensely impractical and must be removed as soon as roads clear.
A car on snow tires can be driven in clear conditions in the ordinary manner without any great loss in performance. On snow, the snow tires's thick, widely-spaced treads will improve traction and stopping. Even better, get snow tires with metal studs built into the tread. These will decrease your stopping distance on ice dramatically, and provide much securer handling under extreme conditions. The only concern here is legality - many jurisdictions ban studded tires to prevent supposed damage to roads (though I think their case is overstated). Without studs, though, snow tires are legal everywhere, and with studs, they're legal in most areas where you'd need them at least in the winter months.
Since snow tires are typically removed every fall and spring, you'll have to pay for tire mounting and wheel balancing twice a year if you only have one set of wheels. The expense can add up over the years. If you've got an older vehicle, it's less expensive to find an extra set of wheels at a salvage yard, have your snow tires mounted on them, and simply change between the two sets whenever you need to. An added benefit is that you can always keep a full-sized spare tire with you and not have to deal with the stock "donuts" if you get a flat.
If you don't take my advice and get a set of studded snow tires (if you'll be driving in a place where you'd need them), at the very least buy a set of chains and keep them in your trunk for emergencies. They're inexpensive, and they may be your only way to get your car out of a bad situation. Many high-elevation highways are impassible in winter on ordinary tires.
The Finnish company Nokian is known for making the best snow tires (this is perhaps not a coincidence), though they tend to be on the expensive side. Kumho makes snow tires almost as good as Nokians, for a significantly lower price. Most of the American manufacturers' products don't perform as well, with the exception of Firestone's trendy "Blizzaks," which can be quite pricey.
As for why I'm placing such an emphasis on tires, last winter I drove from Montana to San Diego in my 1987 Volvo 240. The weather along the trip was unexpectedly extreme, and I encountered one of the worst blizzards I've ever seen while crossing the mountains in Utah along Interstate 15. Dozens of vehicles were stuck at the side of the road, including a good number of fancy 4WD rigs. A Suburban about 100 yards ahead of me skidded and collided with the concrete median barrier. With studded tires on the wheels of my rear-wheel drive Volvo, I made it through the mountain passes at a reasonable speed without even the slightest loss of traction.