Oops, I accidentally made the video at the bottom private; I've fixed that now.
The cows are allowed in an area where the horses can't go, a newly seeded grass field. Horses nip grass off so close to the ground, they'd soon kill off all the vegetation; that's just how they are.
Cows can't graze so close because they have no front teeth on top. They also don't chew their food: they graze, swallow the grass whole, and go somewhere later to relax and regurgitate their food and chew at their leisure. Of course, this is what we call "chewing cud".