There are some very good points above. They brought to mind some safety and convenience points that I have in the back of my mind most of the time, but may be worth adding/summarizing in this thread:
1. Some of the most dangerous conditions occur after partial thawing, especially if the road is clear. You tend to go to the normal speed and you are in trouble if you hit an icy patch in the shade or on a bridge (no insulation from dirt underneath to keep the road surface temperature up).
2. Try to think ahead and put on chains when they make sense (i. e. deep snow but packed from other vehicles, loose snow or badly side-sloped mountain trail up ahead where sliding off=death). It takes only 5-10 minutes to put them on and attach the rubber tensioners. I lay one out in front of the front wheel, drive halfway across the chain, and pull it up the tire front and back. Then I do the other. If you are stuck already, you have a task of (comparatively) epic proportions ahead of you.
3. Making time is completely out of the picture. Staying alive and eventually getting there are the issues. Coming out of Colorado, we were on dirt "roads," sideslopes into a "ditch" 10 feet down, etc. We put chains only on the front of the Ram, none on the trailer. My hunting partner and I fully agreed that low range first gear (3. 5 mph on the gps) was plenty fast enough for the 8 miles or so before the road became "maintained. "
4. Chains are like insurance, and the cheapest is not what you want. When needed, either has to be the best value.
5. Your vehicle sliding off the road, or unable to progress, is only one concern. The 99 bozos out there are a big concern, and avoiding them can be the biggest problem. You may be going up the mountain just fine, and then a half dozen of them are all over the place blocking you. At that point, expeditious stopping and vigilance are the ways to save yourself and your Ram. Usually you can stop OK uphill [although you don't want to slide back down

]. I'm actually more cautious and tend to go slower downhill because it can be harder to come to a stop in the direction I want.
6. Experience is critical. You gain experience by cautious driving and tending toward "excessive" safety precautions [if indeed that is possible since you can't push the reset button and restart the game if you die]. Soon enough you will learn the limits of your setup without exceeding them so much that you can't recover. If you can't think through your next steps to a successful retrieval from danger or being "stuck", get help instead of taking the big chance that you will make the situation worse with risky moves.
7. There are times when it is better, and almost as fast, to wait until environmental conditions improve, instead of "challenging the storm. "