a capite ad calcem
It's hard to really discuss Shadow's appearance since he does such a good job covering himself from head to foot! He is clad primarily in black, but he has a few distinguishing parts of his outfit that are worth looking at. Also, we later get a glimpse of what he looked like before he became an assassin, but sadly there is no Amano artwork or CG stills, so my analysis will have to be based off of a little pixelized figure!
the assassin outfit
For 99% of Final Fantasy VI we see Shadow clad in his assassin gear. It does such a good job of covering him that it's hard to figure out what he's feeling -- for example, if you look at the other characters' sprites, it's obvious when they're excited, sad, etc. Shadow's sprites, on the other hand, all more or less look the same. So no, there is not much to be learned about Shadow's appearance from his pixelized form, except that he's wearing a black jumpsuit, complete with helmet.
Even though Shadow's sprite form is not very complex, Amano actually created a somewhat complex character design for him. Although he is simply wearing a black jumpsuit, his helmet, belt, and boots all feature very distinctive, colorful details. The visor of his helmet features a blue and red pattern that resembles water and flames. Attached to his helmet is a colorful bandana that flows down from the back of his head. It, too, features a blue and red pattern, but it seems to be spotted. Shadow's face is painted black (or at least tinted so as to blend into his helmet), and the only feature that is visible is his eyes. In every picture of him, his eyes carry a fierce, ruthless expression.
As for the rest of his body -- based on the CG renders, Shadow is pretty ripped! He obviously keeps in shape, probably to make his job easier in the long run. His belt is abnormally large (it sort of resembles a belt that someone in the WWF would wear), and it features a blue and red sun design. I have no idea if there's any significance in that, but it looks cool? Some sort of sash extends from the back of his belt, but there is no clear shot of it -- pieces of it show up in various works of art. As for his boots, they're pretty much just blue, and they're tightened to his legs with yellow rope.
shadow's true self
We are fortunate enough to get a glimpse of what Shadow looks like underneath his disguise, and it's not what you'd expect (or at least not what I expected). He looks fairly upstanding and respectable -- his light brown hair is well-maintained and short, and he wears a brown cape over his outfit (which is barely visible). It is hard to imagine how this man went from dressing that way to dressing in a full-body black jumpsuit, but he did!