More than 760,000 people in the northern Great Plains were under a blizzard warning on Monday, as heavy snow and powerful winds pounded the region, creating treacherous road conditions that could last through Tuesday.

Central South Dakota, where more than a foot of snow was possible, was expected to bear the brunt of the storm. Hazardous conditions were also forecast across portions of east-central and southeastern South Dakota, southern North Dakota and Nebraska, said Kyle Weisser, a meteorologist with the National Weather Service in Sioux Falls, S.D.

As of Monday evening, parts of southeastern South Dakota had received up to six inches of snow, but more was expected to fall overnight, said Ashton Robinson Cook, a meteorologist with the Weather Service. Parts of central and northeastern Nebraska, including Martinsburg, Lincoln and Central City, had also received about six inches of snow by Monday evening, though complete snowfall totals were not expected until Tuesday morning for the area, Mr. Cook said.

“Travel could be very difficult to impossible,” meteorologists warned in an advisory, noting that “widespread blowing snow” could significantly reduce visibility.

The South Dakota Department of Transportation said in a news release that conditions were “approaching near zero visibility” on roads covered in snow and ice on Monday afternoon, prompting officials to close parts of Interstate 90 through Tuesday morning.

An accident involving several jackknifed tractor-trailers forced a section of eastbound Interstate 80 near York, Neb., to close for about three hours on Monday afternoon, the Nebraska State Patrol said. There were no injuries in the accident, which was partly caused by blowing snow and slick road conditions, Cody Thomas, a spokesman for the Nebraska State Patrol, said in a statement.

Mr. Thomas said that there had been about 60 “weather-related incidents” on Interstate 80 in Nebraska on Monday, mostly between Lincoln and North Platte.

“We’re urging all travelers to assess whether or not their travel is absolutely necessary before hitting the road,” he said.

Forecasters warned that power outages were possible, particularly in South Dakota, as strong winds could damage trees and knock down power lines. On Monday night, though, there were no reports of widespread power outages.

The heaviest snowfall in central South Dakota was expected from 2 p.m. to 10 p.m. local time, the Weather Service said. Strong winds and snow could linger into the night, especially in the central part of the state, forecasters said. A blizzard warning was in effect through late Tuesday night.

North Dakota and Nebraska will get more freezing rain, causing slick conditions, meteorologists said. Mr. Cook, of the Weather Service, said that Fargo, N.D., had about a quarter of an inch of ice accumulation as of early Monday afternoon, but that amount was likely to increase through the evening as more rain pelted the city of about 120,000 residents.

Blizzard conditions were also expected in northern and northwestern Kansas until early Wednesday morning, as well as in northeastern Colorado through Monday night, according to the Weather Service.

Holiday travelers who had expected to hit the road on Monday afternoon might want to adjust their plans, Mr. Weisser said.

“Depending on which direction you’re going, if you haven’t left yet, you might want to wait until tomorrow,” he said.

Temperatures will begin to rise Monday evening in eastern South Dakota and in parts of Minnesota and Iowa, and driving conditions will improve in those areas, Mr. Weisser said. Strong winds, however, could still be an issue for drivers, he said.

“Even if there’s not a lot of falling snow, you can still have significantly reduced visibility if the wind is blowing 30 to 40 miles an hour,” he said.

The impact on air travel appeared to be relatively modest at the outset of the storm. About 170 flights within, into or out of the United States were canceled as of Monday night, according to FlightAware. About 2,720 flights across the country were delayed. Sioux Falls Regional Airport encouraged travelers to check with their airlines for word of any cancellations or delays.

Eduardo Medina contributed reporting.