My read of the wikipage:
http://ringofbrodgar.com/wiki/KnarrSays 64 liftables + 10x10 inventory.
Animals aren't liftable while they're alive, and carts aren't liftable, but anything you could store in a cart you can store in the Knarr (64 such things, so anything you could store in 16 carts, I should say). The only thing that can move livestock across water that I know of is the raft and I haven't verified that myself, but the raft /can/ move a cart (VERY SLOWLY) and unpacks into two liftables that the cart can haul. For a mobile base with animals you might want to look into the wagon:
http://ringofbrodgar.com/wiki/WagonThe wagon holds 20 liftables, is driven by a single cow/bull or horse, and also has an inventory. The Wagon can also fit on a raft, at least it used to be able to, so you can cross rivers that way. The process is slow, and often annoying, but it work(ed/s):
1) 2 of those 20 liftables are your raft.
2) Unpack raft sections and build raft at water.
3) Load animal, cross, unload.
4) Cross, load wagon, cross, unload.
5) Go run down animal that has wandered off nearby.
6) Hitch animal back up.
7) Break down raft
8) Load raft into wagon
9) Carry on until you find water again, then return to #2.