How do you use the negotiation forum to sell a horse on Howrse?

Go to the Auction tab. On the page it will say sell a horse - the lowest price for the auction is 500e. The Safe Haven will give you 400e in exchange for your horse, or you can sell horses for passes in the Private Sales.

Also, there are two small circles on the top of the horses head on its page: one says rename horse, the other says sell my horse/mare. Click that and it will take you straight to the auctions or private sales page.