Possibly because Cloud is "in darkness" during the first Kingdom Hearts game - he is cooperating with Hades and being pulled deeper into his chain of deals. He doesn't have the wing in Kingdom Hearts II, likely showing that he has changed to fight for the side of good. I think it has to be becuase in heven usally people have wings.But olympus coliseum is kinda like heven. It is also a mirror image to Sephiroth, the "one-winged angel" since he is, technically, a "brother" to Sephiroth due to JENOVA influence. The wing Cloud has is over the shoulder that is lacking a wing on Sephiroth.
A possible reason is to contrast Sephiroth's angelic wing and also as a throwback to Vincent Valentine who was originally supposed to be in the first Kingdom Hearts, which also explains the claw like glove. The reason it was changed in the second game was to highlight Cloud's Advent Children clothing.