I don't think mobs are in any way biome specific (yet).
Mobs are pretty random, so you probably just had a lot of pig and cow herds spawn in your area. It might be necessary to travel further out to find sheep. I had a similar world once where I couldn't find any sheep. I needed to travel quite far so when I did find them I lured the entire herd back to my base (not just two like I normally would).
i don't know. Swamp biomes have a limited amount of animals. I seem to have a large population of pigs then any other animals inside swamps. And I've seen a pig ONCE in a jungle and every single other kind of animal any place else.
Step 1: gather some wheat
Step 2: get a map and a compass, and stuff to survive travelling by foot at night
Step 3: go to an unexplored area, and good luck - you should find sheep patrollmooching around there.
EDIT: sheep don't patrol. Sorry, I sometimes forget this is Minecraft and not Runescape.
Didn't you hear? Jeb made a new dimension! It's called the sheepder.
You need to get ten cobble and put lava in the middle to make the portal.
The boss is called sheepenstein, it has twice the health of the enderdragon.
Sheep spawn like crazy over there.
I've also been having a hard time finding sheep. I usually find them now at the edges of forests and in plains, as well as swampland areas. Just keep looking, and make sure you memorize where your house/area is!