a Barn, or shed, farm terminology varies. Stable is usually reserved for Horses.
Barn, corral, shed, run in, pasture, barnyard, woodlands etc.
The building in which a cow lives can be called a number of things, but I believe the two most known answers for your question are the barn and/or stable.
A barn or shed.
Barn
A barn.
barn
shack
Kraal
An abattoir or slaughter house.
Twelve cows can be called a flink, a dozen head or a herd of cows.
Cows that are milked are referred to as dairy cows. These cows are milked in a barn or a milk house.
Females are called cows and the males are bulls.
There are a whole pile of animals that have females called cows:ElephantsBuffaloBisonElkMooseCaribouDomesticated BovineWhalesRhinocerosesWalruses
They are called herbivores.
Cows give birth to baby cows called calves.
The cows on Moshi Monsters are called MooMoos.
A barn or shed.
A group of 3 cows would be called a "herd of cows". It is a very small herd, but it is technically a herd. Anytime you have a group of cattle it is called a herd.
Female elephants are frequenlty called "cow" elephants.
A maiden doe.