Yes it affects them the same way. We took our horses to the MT mountains a couple of years ago and they struggled a bit with the elevation. Especially when we went up the mountains further in the course of a couple of trail rides. We just took it easy and paid attention to how the horses were handling it. If they needed a break, we dismounted (in a safe area) and relaxed for a bit.
As for prep work. I don't know if this helped a lot, but we just tried to have them in as good as condition as possible. We also did a lot of riding in the lake.
Another point? Elevation makes alcohol effect you MUCH more quickly. I'm talking if you can drink 5 beers and be "ok" you'll be drinking 3 and sh*tcanned. So if you are old enough to drink, and are camping keep that in mind.