I have small tattoos on each wrist. My work has been fine with me showing my tattoos since I've started and I usually end up showing some clients the tattoo I have for my cat, Leo (it's an orange and black striped tattoo of the zodiac symbol for Leo).
I had to cover my wrists up at my previous jobs, but I've never minded because I figured with their placement, I'd have to cover them at work. I fortunately found a workplace that doesn't care if we have tattoos or not. As far as earrings and working with animals, I just personally wouldn't want to wear big hoops and stuff cause I'd be too scared they'd get ripped out. lol