I believe the fatigue factor [horses and men] can not be over stated. I don't think Stuart could have accomplished much in any role assigned him on the 3rd.

IMHO, to expect Stuart to have an impact on the events of the 3rd is similar to the misguided selection of Pettigrew's division to form part of the infantry assault.

It is my understanding that Stuart's cavalry was placed to intercept the retreat of Union forces should Pickett's charge achieve the desired results.