What they do is protect the ears of calves from frostbite. Some are made of yarn, canvas, or fleece.
Calf earmuffs have apparently been around for at least decades, but they're new to me, as I've never lived on a farm or ranch. I gather that they've been invented by various cattle ranchers as the need developed. WMTV News in Madison, Wisconsin describe's one dairy farmer's reinvention of calf earmuffs:
The idea behind "Moo Muffs" came after Poad's family lost their barn in a fire. She was looking for any way she could to keep her newborn calves warm and to avoid frostbite.
"We bought calf jackets and tried to make it work," said Poad.
In addition to calf jackets, she also bought a pair of calf earmuffs. In an effort to try to save money, she asked her aunt, Kim Ewers, if she thought she could make a pair for her. Ewers has been sewing much of her life and and owns her own embroidery business.
"The pair she as talking about was just fleece," said Ewers.
Ewers was afraid if the fleece got wet it could do more damage than good.
"I said, 'Holly if we do [the fleece] and it happens to be snowing, raining, or whatever it will be like putting an ice pack on these calves ears and they might totally fall off,'" said Ewers.
All of last year, the two put their heads together to come up with a design that would be more functional. After some trial and error, the two settled on this particular design.