I run wild and free,   
with oh so much glee.

I can have many fur colors, all are fluffy,  
once you meet me, you'll know I'm a toughie.

My cold soul opens to the kind,  
you'll find me with a warm mind.

I *am* a small one,   
but your heart will be won.

The wild is my life,  
a human home will bring strife.

Here's a hint:
>! This animal is rarely domesticated

Here's another one:
>! I went on a rather large stretch here. The idea was to give the illusion of one animal when it's actually not. Maybe this stretch was too much.