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If you are just looking to get from DC to Denver as quickly as possible, then your best bet is basically get on I-70 and head west. That is true at every point of the year.

First of all, it is a little silly to call a route that is used by thousands of people every day dangerous. There certainly is the chance that you will see some snow or ice, but the reality is that there is no way you can get from DC to Denver in December without having the chance of snow or ice. You cant go far enough south to avoid the risk, plus you would have the chance of seeing snow and ice again as you traveled south from dc and back north to denver! You are much better off sticking with a straightforward route - which is going to be perfectly clear the vast majority of time even in winter - and using the extra time it would take you to drive south to wait out a storm if you do see bad weather.

If weather is good, you could make this drive in as little as 3 days, with overnights around Indianapolis and Topeka.

If it does look like I-70 will be seeing bad weather during the time of your trip, you could look at taking I-80, heading up from Pittsburgh through Cleveland, Chicago, and Omaha, before cutting back down on I-76 as you get back into Colorado. It is roughly the same distance as I-70, and it is possible that it would be far enough north to avoid the weather that is hitting I-70, or even more likely, it could be far enough north where you would be seeing snow instead of ice - and Ill take snow over ice every day of the week. The downside of I-80 is that there are many more tolls, and you do have to deal with Chicagoland traffic which can be frustrating.