The storm has already wreaked havoc in Arizona, leaving at least three people dead and six injured in a series of fiery crashes caused by thick, blowing dust.
The system is also blamed for a death in Nebraska, where a woman was killed after her SUV hit black ice.
A winter storm watch is in effect for most of southeast Colorado, the panhandle of Oklahoma and north Texas through Thursday. Snow is already falling in Salt Lake City.
Blizzard warnings are likely on Christmas Eve in Kansas and other Plains states.
The storm is expected to crawl across the Plains states through Christmas Day, leaving behind plenty of snow.
The potential upside to the massive snow maker, the National Weather Service says the system will give millions of people a white Christmas. The service says virtually the entire central and southern Rockies will get snow, before the storm moves east.