LouannePiccolo already posted one good idea.
I'm quite fond of Old McDonald, prepping the song by teaching the animals with picture cards and asking "A cow says?" Kids answer "MOO!" or the Chinese equivalent. I suggest teaching dog, cat, horse, cow, pig. They should recognize those animals but might not know their names or the sounds they make.
It might be a good idea to find out what the Chinese is for a few of them, and that way you know the kids understand the concept. They're not so different from the Japanese ones that I know. (wang=bark, miao=meow, si si=neigh neigh, mou mou=moo, heng heng=oink)
Once the kids know the voices, introduce the song. Make their only task saying the animal sounds and doing gestures. This can be changed to animal names. My kids only sing E-I-E-I-O and do the gestures
I think anything more complex than this will be lost on 3 year olds.