So there are lots of farm animals... i'm excluding chickens here because they are in the bird section... so we're talking cows sheep horse pigs mice...
This first one is actually for hot plates... but i thought it could be a cute applique as well if you wanted... big one :P for a backpack? don't know what kid likes cows but who knows! anyways the pattern below just treat each square as a single crochet and it should work :)Chisako" I believe...she does wonderful applique patterns for all sorts of things.
These next few sheep patterns you can buy at their respective websites. I just wanted to show them because I could only find this one pattern free.
This next horse is made by "one and two company" and can be bought here
I think this is a cow...
I found this pattern for sale online by "one and two company"
There aren't that many different crochet appliques for barn animals... not sure where you would put them I guess ^^ but who knows what applications you can find for them enjoy!