The shelter for cow ought to be clean and well ventilated.

One word substitute is Byre.

Hutch: a box or cage, typically with a wire mesh front, for keeping rabbits or other small domesticated animals.
Byre: a cowshed.
Hangar: a large building with an extensive floor area, typically for housing aircraft.
Kennel: a small shelter for a dog.
Barracks: a large building or group of buildings used to house soldiers.