We are planning on driving from Denver to DC before Christmas and back again before the New Year. We would be on I70 the entire time, and planning on two overnight stops. In general, what are the weather/road conditions at that time?
Throughout the United States, interstate highways are generally cleared quickly after snowstorms (within 24 hours at most). The only times when road conditions can get unsafe is during or immediately after snow & ice storms — and, of course, we cannot predict in August whether such a storms will occur on a particular day in December.
So the answer is "the weather and roads will probably be OK, but there's always a possibility of bad weather". The best tactics for long-distance road trips in the winter are:
Carefully monitor the long-range weather forecasts starting about a week before your departure. If a storm appears to be brewing, try to rearrange your schedule to depart a day later or a day earlier.
If despite your best efforts, you find yourself caught in a major storm, pull over and find a hotel.
Allow for an extra day or two of travel time. In other words, if you're leaving DC on the 1st and you think you'll be back home on the 3rd, don't schedule important appointments back home for the 4th.