I would haggle, or try to,I have never been very successful, once I had decided I wanted the horse .I wouldn't want to pay for vetting before settling the price.I would only haggle after if the vetting threw something up that I could accept but I felt warranted a discount.What have you found?
when you put a deposit down, you accept the agreed price.
if you then dont want the horse because you cant get any money off, the vendor is well within their rights to keep your deposit if you do not buy the horse!