I noticed this was touched on just briefly, if you start spinning...STOP!!! Wheel speed is not your friend like in mud. What you will do is dig ruts right where your tires are sitting, melt the snow, get stuck and then the melted snow will refreeze and now you are sitting in ice ruts...good luck getting any traction on that!
Yes and no. If you're spinning and not moving, stop. But once you get moving, for Gods sake, DON'T STOP! (when off roading in snow).
Another vote for Nokian tires. They are great in snow and rain.
These are the only winter tires I'll ever use up here (northern Canada). Great tires. The last ones I had, I never did anything serious off road with them, but they were simply amazing on road come winter. The off road stuff I did do, they handled with ease.
Others have listed survival gear (all good stuff, and things you should consider). A couple things they missed are candles (these will heat up a jeep quick should you find yourself staying somewhere longer than anticipated
). Also, either an axe or a saw (I carry a small swede saw). All the times I've been seriously stuck in snow, the hi-lift and saw have been there to save me. The winch is great... but if you don't have one (can't afford one), get the saw. It's a lot easier to jack up the jeep and stick logs under the tires than to dig out the jeep - TRUST ME on this!
Come winter, I carry 2 duffel bags of crap. One contains my tools (not that I know how to use em, but I have em), and the other contains my winter survival gear. Fire starter, sleeping bag, candles, matches, flares, extra winter gear (gloves, toque, etc), wind breaker. My sorels never leave my jeep till the snow is gone. Always carry extra water. If you're going wheeling, carry a few lts. You may not need it... but digging out your jeep is thirsty work.
It can be a lot to carry around... but should you ever get stuck when out and about you'll be thankful. We all say it (then we all do it), but don't wheel alone. At the very least if you do, let others know where you've gone, and when you'll get back (or you'll call em).