Thousands of flights have been cancelled, and power cuts have been reported in some south-eastern states.
Virginia, Georgia, and North and South Carolina declared states of emergency.
The US National Weather Service (NWS) said the storm would hit much of the eastern third of the country over the next two days, with more than 1ft (30cm) of snow expected in some areas.
The huge storm system is approaching the eastern US from the Midwest.
Snow and ice could result in "dangerous travel, power outages, and tree damage", the NWS warned.