On-road: With our big tires, we can get to the bottom most of the time, so starting isn't that big of a deal. If there is ice on the bottom, you'll want to keep wheelspin to a minimum when leaving a light or stop sign. As a general rule, keeping wheelspin down is key, but we all like to have some fun.
Off-road: Treat off-road snow with care when starting. Just like deep mud and sand, feather the clutch and the throttle for the smoothest launch you are capable of. This will help you not dig down into the evil white stuff and maintain forward movement. High-floatation tires are the way to go for deep snow, both on- and off-road.
Whoa Now!
When it comes to stopping in the snow, we can't say it enough: leave more following distance than you might think you need! Whether it's the distance from the soccer-mom mobile or the tree, give yourself enough time. The soccer-mom mobile has an advanced ABS system and will stop better than you. The tree won't go anywhere, so when you hit it, it'll hurt all that much more.
On road: For shallower snow, ice will be the enemy. Black ice, white ice, whatever color it is, it's dangerous. Be especially careful at dusk and just after dark, the areas you drove through earlier will likely have ice on them later. Bridges, due to the cold air cooling them off from below, sometimes have ice on them all day long.
If you do hit ice, don't panic and don't lock up your brakes. It might seem like you'll stop faster if you lock them up, and sometimes you might. However, with the brakes locked up, you've got no control. Pump the pedal like a human-powered antilock brake system. Go somewhere the first snowfall or ice storm and practice pumping the pedal. Take it just to the point where it wants to lockup and pump it there.
Sometimes downshifting helps, if you are smooth with it. If you just dump the clutch to downshift, it'll break you loose. Be smooth with the clutch and downshifting can dramatically decrease stopping distances as well.
Practice the techniques every year because how often do you need to pump the brakes at the beach in the summer?
Off-road: In shallow snow, driving off-road leaves some leniency for braking technique. If you aren't going to go off the trail and are leaving a decent following distance, locking the brakes up can be your friend. With the loose surface under the snow, pumping the brakes can take forever to stop you. Just remember to let up if you start veering off trail so you can steer again.
Deep snow is the equalizer. If they don't plow or salt where you are after a good snowstorm, there isn't much difference between stopping on-road or off-road. Locking the brakes up might seem like a good idea, but if you nosedive into the snow or brake through the crust, you'll have a hard time getting going again. If you have to stop urgently, by all means, lock them up. But when you don't have to stop quickly, try and do it smoothly without locking the brakes up.
Steering (or swerving)
Whether you are on- or off-road, you will find that four-wheel drive really only helps at lower speeds. If you're driving at higher speeds, you might as well take it out of four-wheel drive.
On-road: The biggest gripe in snow is pushing while steering. That is, your wheel is cranked all the way over and you are still going straight. Blipping the throttle can help here. Then again, it can also send you careening that much faster off the embankment. The idea is that you've got to get some weight off the front tires and get them rotating again so they will direct you where you want to go. How you do that changes with the situation. Again, practice.
If you are on ice or icy roads, just leave the Jeep in four-wheel drive. With ice, it'll help you steer where you want to go and also help keep the short-wheelbase Jeep from spinning out.
Off-road: Stay in already-made tracks (as long as they aren't too deep), keep the Jeep in four-wheel drive, and keep the road speed down if you have to make your own tracks. These three things will combine for the best chance of success. Those three things and exponentially increasing horsepower, as the snow gets deeper, will keep you moving.
Some advice from Willie Worthy up in the great white north
* Keep away from trees. The snow melts around trees first because of the heat they put off. The pockets around them will then fill with light wind-driven snow and make for a real trap!
* Snow to snow makes for the best traction. However, ice to snow does not.
* A tire has to grab snow, hold it in for one rotation so that there is snow-to-snow traction, and then clean itself before the snow turns to ice. Voids that are too large will not hold snow. If the voids are too small the snow will not get picked up. Try sticking a snowball to the sidewall of a tire and see how long it stays. Stick snow to some more snow and you have a snowman. There are some exceptions to this because all snow is different, but, generally speaking, a tire that holds snow for that rotation is better all around than one that totally cleans out like a Super Swamper Bogger will. They put on great snow shows, but don't get on a sidehill with them on icy snow!
* You can go downhill a lot easier than uphill. What this means is that maybe you have gone in on a trail that was downhill most of the way, but you just may not be able to get back out.
* Chains work great in icy snow, but make sure that there is enough clearance for the chains and that they are super tight. Tie the chains on with heavy rope or really heavy tarp tie-downs. Those cheap spring and lightweight rubber tension devices just don't do it with big chains that we need for our tires. Double the crosslinks in the chain for safety.