I work with two Appaloosas; My Easy Shaygetz and Big John.
With these two I have learned that Appys are very smart and, like any horse, get bored easily. These specific two don't like doing anything too far out of the norm (such as being in the front of the trail line, which they rarely do). They commonly test us workers, seeing if they can gain "rank."
Other times they play games with us. Shay is famous for stealing hats and bolting with them. John is more apt to search your pockets. They aren't mean-spirited, but certainly have their "bad days" (who doesn't?).
They are very sturdy, like Tinyliny said. In addition to eye problems (which, if I'm not mistaken, can be a cause from their 'eye whites' being so prominent), they also tend to be flat-footed. Shay needs special pads under his shoes to protect the soles and frogs of his feet.