Take everything they say with a grain of salt. Have YOUR vet do a pre-purchase exam on the horse before you buy it.
It's surprisingly common for people to buy a horse only to find out that it's WAY older (or sometimes way younger) than the seller said, either because the seller honestly didn't know the horse's age or because they knew no one would want to buy a horse that old.
Ask the seller to show you everything they've claimed the horse can do, even if you don't plan on doing it yourself. If they say the horse jumps 3'6", have the demo it. OK with clippers? Then have them clip (or pretend to clip) to demonstrate. Great on the trail? Haul the horse out to a trail if there's not one on their property. Visit multiple times if necessary.
Be sure to handle the horse yourself for catching, grooming, and tacking up. Don't even let the seller hold the horse's head- have them stand off the side.
And bring along a trusted friend who is knowledgeable if at all possible!