We found an article in the Klondike Book that contained some information about farm animals. The Shaman helped us translate it. Here's what we learned:

You can make feed for your animals in the Barn.
Once it's ready and you've collected it, it goes to your Market.
After that, open the Animals tab, then the Food tab, and drag the feeder/hay from the Market to your Home Station.

CHICKEN
- Gives chicken eggs that you can use to complete orders and for crafts,
- Eats feeder,
- Turns into a golden statue after 16 meals.

COW
- Gives milk that you can use to complete orders and for crafts,
- Eats hay,
- Turns into a golden statue after 24 meals.

SHEEP
(available from lvl 17)
- Gives wool that you can use to complete orders,
- Eats sheep feed,
- Turns into a golden statue after 24 meals.

GOOSE
(available from lvl 21)
- Gives feathers and eggs that you can use to complete orders,
- Eats goose feed,
- Turns into a golden statue after 16 meals.

PIG
(available from lvl 23)
- Gives truffles that you can use to complete orders,
- Eats pig feed,
- Turns into a golden statue after 10 meals;

You can also purchase Tribal and Purebred animals for emeralds at the Market: they give you more produce, and you can have an unlimited number of them. Animals that you purchased for emeralds turn into golden statues full of prizes as well.