Thinking mainly of French cavalry here.
Would a General de Brigade in charge of (say) a dragoon brigade of 2 regiments, charge with them? Personally, I would have thought so. I can see that a General de Division or a Corps commander would have other things to do and other troops to manage, but when you have committed your entire and not very large command to the charge, would you really hang back?
With regard to uniforms ... Would the General commanding (for instance) a dragoon brigade (not exactly a large formation), wear dragoon uniform? I believe there were Generals of cuirassiers (a breastplate of one such is preserved), although am unsure at what level this appointment existed.