"This actually could be a historic storm for folks across these areas," Dean said Wednesday on "FOX & friends."
"We could see 6 to 12, to 24 inches of snow, winds in excess of 35, even 50 mph," Dean added. "Travel is going to be impossible in some of these areas."
The National Weather Service's Weather Prediction Center said the storm system will move over the Rockies and into the Northern Plains by Wednesday night, bringing heavy and wet snow to the region.
"A swath of 1 to 2 feet of snow is forecast for the Central/Northern Plains and into Western Minnesota through Thursday evening, with locally higher amounts," the NWS said.
The highest amount of snow is expected to fall across South Dakota, but the combination of snow and strong winds throughout the region will make traffic "difficult to impossible" as visibility drops to "near zero."
There is also the potential for sleet and freezing rain with accumulating ice near the border of Iowa and Minnesota, which may lead to power outages and dangerous travel.
The storm could be similar to last month's "bomb cyclone" -- an unusual weather phenomenon in which air pressure plummets at least 24 millibars in 24 hours and a storm strengthens explosively -- that created devastating flooding across the Midwest.
While this latest storm may not intensify fast enough to that category, Colorado State Climatologist Russ Schumacher told the Associated Press it "will be near record intensity for April for this area."
Besides heavy snow, there is the potential for severe thunderstorms in warmer areas across the Midwest, according to Dean.
Nebraska is not expecting a repeat of the catastrophic flooding it experienced last month because the ground is no longer frozen and ice has melted from the rivers, though there might be localized flooding across the state, according to weather service meteorologist Van DeWald in Omaha. The biggest threat will remain along the already swollen Missouri River, he said.
"It's really just going to exacerbate that flooding and prolong it," he said. "We're probably looking at that surge hitting those Missouri River areas in Nebraska and Iowa three to five days after the storm."
In northwest Missouri's Holt County, where the raging Missouri River ravaged roads and highways, Emergency Management Director Tom Bullock is urging residents to be prepared to get out if another surge of water arrives after this week's storm.
"We don't have any protection," he told the AP. "Our levees are all broke."
The Associated Press contributed to this report.