I had been googling b/c I wanted some paper craft animals.
I found out that the IPad has an app, Foldify (the 2nd one has the animals), that is only $2.99 and has 10 animals to cut out and fold. Most animals are only 2 pieces (the head and body) and most are fairly easy to cut out (except for ones like the turtle that just has a lot of curves in it) and the folding really isn't too intricate. There are the pre-colored ones that come with the app. Additionally, you can actually color the animals yourself in the app and put funny eyes, mustaches, eyebrows, scales, etc, on them. There are also ones that people have colored and uploaded that you can use (some of them are really great).
Once you've done all your changes, you just e-mail it to yourself, print out, cut and fold. I'm using them for centerpieces, plus I've e-mailed some of the blank ones for the kids to color and cut out on.
This is different from the Tiny Paper Zoo app, which was way more difficult. I think Foldify could be used for as young as 3 really, depending on the level of supervision/input you want to have. The coloring part could be difficult for a youngster, but their pre-made ones would be pretty easy.