What is your property like? Some people spread manure in pastures for fertilizer (although you have to be careful about worms!). You can dump it somewhere on the property that isn't being used. I like the idea of it being hauled off property, but that's not always doable.
Mud is inevitable most of the time. You can dump crusher dust or gravel in the paddocks, especially in high traffic areas such as gates. Dirt and hay will turn into muck, which leads to mud fever! It's also good for hooves to walk on hard ground.
I prefer horses to live outside! They can come and go as they please. There's really no need to stall horses as long as they can get out of the wind and weather when they feel like it. Horses who live outside are healthier and happier. Even injured horses are often better being allowed to walk around rather than being stalled. You can screw in a ring so you can tie your horse up in there. It's nice to have a barn with cross-ties though (even if there is no stall) for things like vet/farrier appointments, grooming, tacking, etc. You'll also need a place to store hay, feed, and equipment.