When a similar blizzard happened near Fort Collins, the sheep were better able to survive than the cattle, though of course losses were still awful:
"Such was the scene before the 'Blizzard of 1949' hit northern Colorado and southern Wyoming. The land that is now SPNA
was then owned by the Warren Livestock Company (WLC), founded in 1883 by Francis E. Warren. Former WLC foreman David Cook recounted in his memoirs of the blizzard how the sheep that had been 'snowed under' were able to survive for as long as ten days and could be located by steam rising from their nostrils through holes in the snow. In spite of being semi-frozen and unable to move when they were discovered, 'they could be revived by rubbing and working their muscles.' Other animals 'froze to death while standing,' he remembered."
My Mongolian colleagues at CSU talk about "dzuds," white-out blizzards that can dump enough snow to bury yurts. They've had a few in the last decade and the pictures are astonishing. Even the animals bred for that climate for millennia die by the millions in a bad year.
Best wishes to the ranchers and shepherds of South Dakota during such a difficult time.
"I think our governments will remain virtuous for many centuries; as long as they are chiefly agricultural."