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First the good stuff! I-70 through central Colorado and Utah is one of the most beautiful roads anywhere. And I-15 will take you near to some amazing parks, including Zion National Park, Lake Mead National Recreation Area, and the Mojave National Preserve. The drive can be made in as little as two relatively easy but full days if you forego major tourist stops, including Las Vegas.
Now the stuff you'll have to worry about or plan for because there's really nothing much you can do about it. I-70 through the Rockies can and does see some terrible weather in the winter. The very best way to deal with that is to avoid it, not by driving around it in space but in time. The road crews along I-70 are some of the best in the country. All those ritzy ski resorts depend on I-70 being kept open throughout the winter, but that's not going to happen in the midst of a given storm. So your best bet is to have enough available for your drive (3-4 days) that if the weather turns against you, you can just sit it out, let the road cress do their work, and only get back on the road when the weather has cleared and the roads are fully open. That may be a day or so in the worst of cases.
Think of it this way. If you have fur days for the drive and the first day is clear and you get over the Rockies and into Utah, you can spend your 'extra' time seeing some of the great parks along the way. If there is bad weather at the start of your trip, then you either wait it out in Denver or at some beautiful mountain town, enjoy the beauty of fresh mountain snow, and then get back on the road when you can, safe and still with plenty of time to get to San Diego.
AZBuck