You'd need a pack horse, but I'm not sure how authentic that would be. Marching cavalries typically didn't carry hay, but foraged. Lacking forage, they relied on grain, but the grain was pretty much "emergency rations".
A horse can't possibly carry enough hay for itself for five days and carry a rider as well. With no forage an average horse will need 20 pounds of hay a day, more if he's carrying a rider in the mountains all day, plus plenty of grain to avoid severe weight loss, so you're talking 100 pounds of hay for five days for one horse. A pack horse could carry two bales, each about 50 or 60 pounds, and all the grain needed as well - but the pack horse needs to eat too. So there's just a big logistical problem with the idea of packing hay.
I'm guessing the only way to make a trip like that is to have a pack horse packing nothing but grain, as grain is very concentrated food. I don't know anything about oats. The modern grain mixes we feed our horses are very different from what was fed them 100 + years ago. I do know that feeding a horse nothing but grain for five days straight is very hard on their digestive system, but some horses would handle it okay, others would become very ill and possibly die from it.
I'd google something like "marching cavalry food for horses", and see what pops up. Nowadays we'd just take a few hundred pounds of hay in our truck, park as close to the campsite as possible, and take one pack horse out for a day or two, at most. That's extremely different from what would have been done by an army on horseback in the 1800s. You might also try googling "primitive camping horseback", and see if that gives you any ideas.