I LIVE in the mountains of Colorado, and we have to function up here year-round, even with snow. CDOT (CO Dept of Transportation) is really good about keeping roads clear and open. If there is an actual storm going on, you might want to wait it out and just find a place to park until it passes. As soon as the snow stops, the CDOT plows will have most of it off pretty quickly.
Wolf Creek Pass is really not that scary, but it does get the most snow in the state. Monarch Pass on US50 a bit further north is tough during an actual storm, but as long as you take it easy, it is actually not that bad--and it is relatively short (I believe it is about 25 miles all the way from one side to the other). The one challenge with Monarch is that you have to go through Gunnison--which can be the coldest spot on the planet at times. Temps as low as -25 during the day are not uncommon in late December, so do NOT have any water in any tanks on your way through there.
The bottom line is, if it is actually snowing or any of the passes have chain restrictions, you are driving in your living room. Just stop and take a break until the storm ends and the restrictions have been lifted, and you will be just fine. Make SURE you keep an eye on the weather, though, as driving mountain passes during a storm is not fun......
