I think you should offer what you think he's worth. If your budget is 13k and you think he's worth that then you should offer that. If you get there and you like and want him, but think he's worth 10k, then offer that. The worst that will happen is they are offended and/or say no. It's not a big deal...just move on and find a different horse. I think people are so worried about offending others that they don't say what they want or need to say. And people get offended over the littlest things. If they start to sound offended just say that you understand and will definatley think on it. Just act like they are completely right.
For 15k in this economy the horse better be what you want and what you need at the price you are willing to pay. I don't think they'd have a problem lowering the price 2k to a good home that will enjoy him.