I am an animal, but which one?

Question

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.

Answer 1

Is it

A fox?

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

A fox usually is hardly tamed.

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

Foxes are fluffy. They can survive in very cold places so they are tough(arctic fox) and have different fur colours like white, brown and red.

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

Foxes can live in cold places (cold soul) but they can be warm?

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

Foxes are small. Foxes I think are sorta cute?

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

Foxes are wild animals.

Or maybe (2nd answer)

A wolf?

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

A wolf usually isn't as easily tamed.

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

A wolves can be fluffy. They are usually thought to be tough animals and will fight(tough).

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

Wolves can be found in colder places, but they are warm-blooded creatures.

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

Wolves are smallish compared to things like bears and people.

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

Wolves might act aggresive to people and they are usually wild.

Bonus hint for either

the acrostic spell IIMIT which might be I'm it and their picture looks wolfy and foxish(their pic has 2 tails though)?

Answer 2

Okay this is kind of a stretch but here goes nothing:

A cat?

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

A cat usually isn't as easily tamed (compared to a dog) and even when domesticated, can tend to spend more times outdoor doing whatever that they're doing.

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

A cat (sometimes) is really fluffy! But if you try to pet them they scratch you. A lot. (Speaking from personal experience here, y'all)

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

Cats are notorious for being my aloof than a dog, but with enough kindness and care, they'll warm up to you. You have to be able to care for the cat (a "warm mind").

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

Kittens are small. Actually, house cats aren't exactly big creatures. And what is more irresistible than a cute cuddly kitten? (Who can scratch you....)

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

Cats were originally wild animals. Also cats are known for fighting with dogs, the most common household pet. And cats scratch furniture. And other things. So it can bring strife.

Like I said, I don't know, I'm just throwing ideas out there.