Some people.might think this is a strange idea, but if you just want an inexpensive horse to ride and pack through the mountains, why not consider an off the track Standardbred, that is if you or your family members have any experience training horses. You might be able to find one that has been used as a brood mare for a few years for under a grand, sometimes a lot less- heck, one of the farms I worked for as a kid used to almost give away the broodmares who'd had 4 or 5 colts that didn't make money.
I've made several of them into riding horses, just make sure the one you pick isn't retired because it broke down on the track. They can be incredibly tough animals, they're usually easy to train for riding, calm around vehicles (if they've been on the track) and they have a lot of endurance (which doesn't mean that you won't have to keep them in condition). A horse that's been used to pull a sulky will tend to tolerate a lot. They're used to things bouncing along behind them, they've worn a harness, so saddle training and packing isn't usually a difficult step for them. Oh, and if you plan to do more than walk, buy a pacer that didn't need hobbles. For gaits it will walk, it will pace, and it will lope (after some work). A trotter will have a walk and a huge trot (not what you want on the trail) and usually a very short strided gallop instead of a lope.
I'm not saying it's the best option, Just a thought for the DIY bargain hunter.
I've always enjoyed putting in the work myself, but I grew up with horses and there were decades of my life when I probably spent more time on a horse than I did on my own feet. Everyone has different expectations and experiences so ymmv.