I am currently livestock free, but this is temporary. I am raiding the Volcano excessively, so i have to depart early in the morning and spend most of the day there, working my way to the 9th level's chest; until i collect all items (i still need Phoenix Ring and Dragontooth Hammer). Sold my animals in year 3 and now i am in year 7! I estimate waiting until ~year 10 or so, because i also need to finalize my farm layout, plus i need to skip days quickly for certain vendors' goods, first!
Raising and maintaining animals is good and all, but requires much time, even for a quick petting; let alone gathering their goods and processing them. In my previous-previous save, i constructed a big shed full of mayonnaise, cheese and wool machines complete with hoppers, because animals products stockpiled in the hundreds, while i was after other things (and still couldn't find time, even for picking up the automatically produced items)!
From what i gather, they should be the finishing touch, unless your economy revolves around animals.