horses are a huge target. If shtf, people will be eating horses. A decent rifleman, with a scope, can hit a horse easily from 600 yds away. Any sort of wound will render the horse unable to do anything, for many weeks, and normally, such a hit will prove fatal in days or hours, if not minutes. A 1500 lbs horse is 800 lbs of meat, 600 lbs of jerky, enough to get a family thru a year of shtf, given a bit of gillnetting, trotlining, snaring, boxtrapping, and knowledge of wild edible plants. So don't kid yourself about horses for shtf, either keeping them or riding them. They are noisy, won't remain still. they get sick or hurt, want to breed, etc. A mountain bicycle (or 3-4) are much more like what is needed. You can hide a bike under a bush, and it will STAY THERE,
Nobody will shoot it or want to eat it. With a 1/2 can of "slime" in each tire, it won't get flats, and there's solid rubber bike tires. You can walk along side of it, with 30 lbs on your back and 120 lbs on the bike, thru some really bad terrain, and if you get a downhill slope, you can coast. If you get a road-like surface, you can pedal.