Animals will seek shelter if its available, but fields are a man made thing, much of the planet used to be covered in trees but the agrarian society started off this planets deforestation, which is being repeated in parts of the world today like the Amazon.
Not only that but that shed poop besides being compostable also served as a source of fire fuel which is still used today in parts of Africa.
Ideally we would have plenty of pasture for animals to graze on, because even dairy herds will go and get milked when they want and not when the farmer schedules. This is a behaviour that's been seen in some dairy factory farms with automated milkers, the elephant in the room is we dont have enough planet earths in which to feed todays human and pet population unless we go all vegetarian or ramp up the production of lab grown meat.
In 2008 a US lifestyle needed 4 or 5 planet earths, today some suggestions put that as high as 8 planet earths, where as UK and Europe have remained mainly the same, ie a UK lifestyle needs 2.5 planet Earths and a European lifestyle needs 2 planet Earths.
That's the elephant in the room!