I live in the new forest, where both horses and cows roam freely. They seem to get on okay and I often see mixed herds grazing provided neither of them has new born young, they seem to keep more to themselves then
Presumably because more farmers keep cows and / or sheep than keep horses.
Horses are more often in a field belonging to either the owner or the livery stables.
They can and do graze together.
Also cows and sheep thrive better on different lenght of grass, sheep are happy on very short turf while cows prefer longer.
I think it is also to do with the different parasites (worms etc, that can be transfered) you have to worm horses but I have never seen a cow being wormed??!!
apparently donkeys like cows and herd well together. The donkeys end up protecting the cows from predators - so people say the donkeys think they are cows - see q above about the dog that thinks it is a cat.