bundled up against Aspen's winter chill, but caused a firestorm over her fur coat's authenticity -- and we've got the answer to the question: real or faux?

The reality star stepped out Thursday night in a thick black and gray "fur" coat for some sister bonding with and ... who were also tagging along, and looking fashionable.

In news that'll shock no one, the coat's causing a lot of debate online .

.. 'cause it looks pretty dang real -- which is weird since Khloe's spoken out in support of animal rights in the past. In fact, she did a whole ass campaign on it way back in the day ... an edgy one at that.

'Memba, KK stripped buck naked for a PETA campaign back in 2008 ... with the tagline that she'd "rather go naked" than wear fur -- and hey, no complaints here on that front!!!

She seemingly had a falling out with PETA a few years later after they threw a flour bomb at Kim on a red carpet ...

saying PETA lied about their relationship with the culprit -- and she expressed disappointment about their support for the lady who did it.

She added at the time, "I've been a vocal supporter of PETA for a long time but I have also been very vocal about anti-bullying, so this was a huge disappointment for me."

Anyway, we figured out whether this thing is the real McCoy or not -- sources with direct knowledge are telling us it's actually faux fur -- so feel free to put down your pitchforks, folks.

The KarJenners do this kinda thing all the time BTW -- Kendall wore what looked like fur in Aspen after her split with and Kylie seemingly wore a real fur scarf on a trip ... basically, the ladies kinda stir up drama on this front now and then.

No real fur in this case though ... so Khloe's in the clear.