Corinnebelle:
We do say to "clam up" which means to stay quiet.
In China you see lion statues at most historic sites and one is usually female and the other male. You can tell them apart because the male will have a paw on a ball and the female has a paw on a cub. Also in China for Spring Festival (Chinese New Years) they have a mythical beast called Nian who looks like a dragon but it's a dragon. Dragons can be good, but Nian is never good. At a Chinese wedding the Phoenix represents the woman whereas the Dragon is the man.
We have many sayings using animals in English
Stubborn as a mule, sly as a fox, strutting like a peacock, sneaky as a snake, stinky as a skunk, feisty like a badger, to be as happy as a pig in mud, docile as a lamb, or being led to the slaughter like a lamb. Dumb as a turkey (the domestic ones).