Cute, cute, cute! I think you don't want to do too many games or activities since the birthday girl and most of the guests are only 2, so I would pick a few you really like. If it were me, I'd stick with 2, maybe 3 things to do.
I would suggest tatoos, I'm sure you can find farm animal ones! They are always a big hit at all my parties. You have some good suggestions for games, pin the tail on the donkey is pretty cute! You could also do some sort of 'barn' dance..even if it's just playing music and letting them dance around! I also saw on Oriental Trading Co some balloons that look like pigs, chickens, and cows. Cute!
As far as snacks and food I would definitely go with a lot of fruits and veggies, it goes with the theme! They do make animal crackers in barn animals, you may just have to look for them or Google them. You could do toasted coconut stacks...or even better dip chow mein noodles in chocolate and then stack them up in big blobs to look like hay stacks. You can buy Baker's chocolate in a little tub you just pop in the microwave in the choc. chip aisle, I've used them before and they're great! If your child likes Jello you could also do a jello mold in the theme...either find a cake pan that is farmish or just use a round cake pan and some strawberry jello (greased and sugared of course) and then decorate it to look like a pig face with some cut up fruit or piped whipped cream.
For goody bags you could do little figurines or farm animal puppets. I bet you could also find little puzzles with a farm theme.
Check out the Oriental Trading Co website for other inspiration and cheap things to go with your theme!