By Carey Gillam

(Reuters) - The storm was just so sudden, South Dakota cattle rancher Kathy Jobgen remembers.

A freezing rain, followed by an avalanche of four feet of snow and winds of 70 miles an hour, hit thousands of cattle still grazing on "summer pastures" at a time when the animals had not yet grown their protective winter coats and were ill prepared for the harsh conditions.

Swirling snow lodged in some of the animals' lungs, suffocating them. Hypothermia killed more. And others were caught in gullies, or plunged off slickened rock ledges, livestock experts said.

"I've been in this business 50 years and I've never seen anything like this," said Jobgen, who estimated her family lost nearly half of its herd of 350 when the storm swept through October 3-5. "The vision of seeing all these cattle dead is something you can't wipe out of our eyes."

South Dakota had the sixth-largest cattle herd in the United States with some 3.85 million head in January 2013, according to the U.S. Agriculture Department. Most of those are in the western part of the state, where the storm struck, leaving carcasses strewn on the Plains and hitting ranchers with tens of millions of dollars in losses.

Dustin Oedekoven, South Dakota state veterinarian, said reports to his office so far total about 3,300 head of cattle dead. But he estimates the number will eventually reach 20,000.

"It really is going to take a hit on the industry here," Oedekoven said.

South Dakota Governor Dennis Daugaard on Friday issued an executive order allowing truckers carrying cattle carcasses in the state to exceed normal weight limits to help expedite removal of the dead animals.

"The weekend blizzard already has caused untold devastation," the governor said in a statement. "The number of livestock actually lost in the storm isn't certain, but it will range in the thousands of head."

Ranchers are both trying to bury animals and haul them to roadways where renderers will remove the bodies. But while the snow melt has allowed for roadways to be cleared, the pastures in many areas are flooded or too muddy to access, making it hard to collect carcasses and to care for surviving animals.

Silvia Christen, executive director of the South Dakota Stockgrowers Association, said most cattle ranchers do not carry private insurance policies because they are cost prohibitive and have exclusions that would have ruled out coverage in this situation anyway.

She said the ranchers' only financial assistance would be found in a disaster program that is part of a proposed U.S. farm bill. But the U.S. government shutdown and delays in passing a new farm bill have left ranchers with no assistance.

Ranchers are not able to even consult with their U.S. Farm Service Agency representatives on how to document their cattle losses, since the FSA workers are on furlough because of the shutdown, she said.

Christen said each calf lost has a market value of roughly $800-$900 and each cow is valued at about $1,800, so the total losses could easily be in the tens of millions of dollars.

"This is a major financial loss for these ranchers," she said. As well, she said, the emotional loss has been wrenching.

"The ranchers care deeply for these animals. To find so many of them have perished in this storm is really emotionally devastating," she said.

The South Dakota disaster could compound an already tight U.S. cattle supply situation in the spring, which could keep beef prices at or near record levels, Chicago Mercantile Exchange livestock traders said on Monday.

The spring is when a lot of the calves that were lost would have come to market. That is likely to help put a floor beneath prices for April 2014 delivery of feeder cattle. The April contract settled on Monday at 135.650 cents per pound, up 0.375 cent.

U.S. Senator Tim Johnson, a South Dakota Democrat, has been urging Congress to reopen the government so livestock disaster aid programs can move forward. Johnson's spokesman, Perry Plumart, said Monday that the senator's office has been in touch with ranchers from around the state and heard losses as high as 80,000 animals.

Gary Cammack, a rancher from Union Center, South Dakota, who runs about 500 cows on 10,000 acres, said the suddenness and severity of the storm caught everyone off guard. So far, Cammack and his family have counted about 120 animals dead.

"Within 24 hours after the storm broke, we knew it was going to be bad. When we went out looking for them, there were cattle stacked up in every fence corner. They just gave up and died there," said Cammack.

(Reporting By Carey Gillam in Kansas City; Additional reporting by Theopolis Waters in Chicago; Editing by Greg McCune and Steve Orlofsky)