Ask if the horse has been vetted recently and if they have any x-rays from that vetting.
Last time I was horse shopping, we went to look at a horse that was some distance away. After we decided we liked the horse and wanted to have it vetted, the seller said, oh, he was vetted 3 months ago and we have x-rays, do you want them? We sent them to our vet and he found a couple of things that he felt made the horse not suitable for the intended use.
I don’t think the seller was deliberately trying to hide anything, I think they genuinely didn’t view those things as a concern. But if we had been able to see the x-rays first, we could have saved ourselves a 2 day trip.
Also, really think about what skills you expect this horse to have and ask the seller about them. We drove 5-freakin’-hours (one way) to look at a horse that had me saying, “no, no, no, no, no” after about 15 minutes in the saddle. It made me realize that my view of “things that are so fundamental that you can assume a horse at this level can do them” is not even close to universal. And it wasn’t that the seller had been misleading, it was that I failed to check my assumptions.