He has solid bone, a solid mind, and, although he has faults, with proper work there's no reason he won't be a great trail horse/ fun horse. Because of his build I would definitely work on strengthening his top line and back, though. Going up and down hills is one way to do this- it makes him engage his hind end and use his back. There are plenty of exercises you could do with him.
My mom's mare is built similarly (I've attached a picture of her so you can see how she's built). She's in her 20's, and doing perfectly fine. She has arthritis in her shoulder and hips from her old age, but she can still be ridden on the trails and loves it very much. So, for what you want to do, I think he's perfectly suitable.
An important thing to consider are his feet, though... Have you gotten to look at his feet yet?
Yes that was the first thing we did with him, the farrier saw nothing wrong, no signs of navicular, very nice hoof walls, and saw immediate improvement in his gait after the trimming. He's not registered, but the vet will be out in a few days to give him a look over.
I don't think he looks that old... I can believe that he's 10. I really do believe the sway back is just because of his build and not being worked accordingly, I've seen a lot of young horses that are used just for packing/trails/joy riding that have backs like this for the same reasons. My friend's mom has an arabian, he's maybe 11 or 12, and he's got a really bad sway back because she doesn't know how to work him properly and has never had a lesson.
Lordosis (sway back) can appear even in foals and yearlings who have had no work... It isn't always work related at all. Some speculation is it is genetic, others suggest it might be impacted by environment or even diet.
Not really a fan of this guy. His color's pretty and he looks sweet, but that's about the best thing I see...
Very long back and neck with small hindquarters, super short front legs, and the hind legs aren't much better. Pasterns are very short and upright, and his shoulder angle is very steep as well. Croup is also sloped very steeply, not smooth and rounded like it should be. He also looks wasp-waisted and downhill, even though he's got pretty high withers for a QH.
I don't know if I'd trust this guy to stay sound, and it doesn't look like he'd be a very smooth ride on the trails. Even for just a trail horse, I think you could find a nicer horse.