Because no southern jury would convict at that time???
One supposed southern “war criminal” - Henry Wirz, commander of the Camp Sumter POW facility near Andersonville, Georgia - was tried and convicted by a military commission in Washington D.C. shortly after the war. He was killed by union authorities.
There is no reason to believe victorious union authorities did not have the same power over Forrest.
“Because no southern jury would convict at that time???”
Most likely he would have faced a military commission instead of civilian authorities as was Captain Wirz, commander of the Andersonville pow camp.
Wirz was captured, shipped to D.C. and tried, hanged and buried there.
https://en.m.wikipedia.org/wiki/Henry_Wirz