I have 4 goats, 2 miniature horses, and a miniature mule. The goats were here first. When we got the mule, she spent the first week terrorizing the goats. The first day, I had to fish one of them out of the pond twice (she got stuck in the mud), and goats hate water! By the time we got the first horse, things had calmed down considerably, and a couple of the goats were actually picking on the horse. That, too, decreased with time. The last mini was 8 months old when she came here, and at least one goat delighted in butting her at every opportunity. Fortunately, she is much faster than the goats, and didn't give them many chances! She is now 2 years old, and they all pretty much ignore each other, unless there is food to fight over (everyone get separated at feeding time!).
What I'm trying to say is, it may not go smoothly, it depends on the horse and the goat. Both are herd animals, and prefer company of their own kind, but they may accept the other as a substitute.
Whether your one acre of pasture will support both a goat and a mini will depend on the condition of the grass. Really good pasture might be able to do it, poor pasture will go downhill in a hurry, until there won't be enough grass to support a rabbit! I'm betting that you'd have to do some supplementing with hay, at least part of the time (cooler seasons, dry periods, any time the grass isn't growing well). Minis can be rough on fences, but so can goats, so IMO if your fence is pretty much goat proof, it should be enough to contain a mini, too.
tell me everything about them
I could type all morning, and not be able to tell you everything about them! They need shots, worming, hoof care, etc, etc, the same as a big horse, with a few things that need to be done differently because of the mini's small size. There is a forum dedicated to miniature horses, trust me, you can find more information than you ever imagined there!