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Do you mean an actual hunt horse or one you think might do good at hunting ? The former do not normally need to be advertised and nobody really needs the latter.
Wow, really, thanks, that was so helpful!!!
She’s absolutely correct.
But … I’ve got a stable full of hunters that were winnowed down from a procession of horses thru my barn that identified themselves early upon their arrival as likely-to-be-reasonable (to excellent) field hunters, with the correct training/exposure. So, while a ‘field hunter’ wth no hunt experience has no market, in the correct market, to the corrrect horseman, at a price that reflects the relative lack of experience (hunting, I mean) you might find someone to take a flyer on the horse.
In that case, ‘advertising’ would be telling good professionals that hunt with your local clubs about ithe horse and see if anyone is looking for a prospect.
The best advertisement for a hunt horse is to actually take him hunting. I have sold a handful of hunters this way–all for more then I would have gotten if I would have just stuck them online somewhere. If you think he will be a good hilltopper, take him out–or have someone else do it. That way you can market him and he can get the experience at the same time 
