Make a video on YouTube and post it on Facebook as a link. Otherwise it isn't allowed. But you can still list horses. I saw one that made me laugh. Lawnmower and little weed eater for sale.... Something else equally amusing.
For a barrel horse, pay for an ad on Barrel Horse World. Do be advised that you will get some spam emails. They don't have anything to "make sure you are a real person" before getting to send an email, so the spam bots like it.
NOT recommending Craigslist but do you have any similar websites in your area? We have a local community website that lets you post ads for free, and very popular for horses in my area.
You *can* still sell on FB, but you have to be careful. There's still quite a few pages out there.
Any of the barrel horse sites would be my recommendation, just make sure to look at some ads first so you price competitively. I've been looking on CL a bit recently, but Equine Now tends to have the same ads for my area at least.