Here’s Ranger Dan Vermilya giving a really outstanding lecture on what four of the post-Civil War presidents who were Civil War veterans did in the Civil War. He did not include U.S. Grant or Andrew Johnson, as they are fairly well known. He focuses on Rutherford B. Hayes, James A. Garfield, Benjamin Harrison, and William McKinley. I think you’ll agree Dan did a terrific job.
The Civil War Careers of Post-Civil War Presidents: Gettysburg Winter Lecture