I think on should use the grandfather clause, 1939, to determine if they are a descendant of a Free Person.
If the veterans were qualified to vote prior to 1866, their descendants were also qualified. Thus, in effect, if a person's grandfather could vote, he could vote without further restrictions.
If your grandfather was a slave, than you are a descendant of a slave. If your grandfather obtained his freedom, you are still a descendant of a slave.
If your grandfather was a free born person, than you are a descendant of a a free born person.
By the way, the grandfather clause was the last major issue that the court got into which touched slavery, the issue of voting.
Harrison Thomas LaTour
LaTour Genealogical Collection
http://www.latourgenealogicalcollection.org/My_Homepage_Files/Page12.html