Beginner here, confused about tamed animals/pens/cages/etc.

Hey all, I've become addicted to DF after reading the NYT article on the game, and I've been doing "decent" so far (although I still have tons of questions). One thing that completely eludes me is the whole tamed animal industry. Here goes:

I want cows/horses/etc. for their meat/hides/bones, so I set them to a pasture outside and occasionally butcher one at a sustainable rate. So far, so good.

Goblins arrive and butcher everything outside. Damn it.

Is there a better way to have a tamed animal industry? Can I put pastures underground? Can I stuff all my animals in cages and have them completely fed *and * reproduce for me? (cages I've found are apparently very "magical" objects). Is there a best animal you guys use for your economy?