I found Samuel N. Dunning on the 1890 Veterans Schedule that indicated he served was a Private in Co D, 8th Illinois Cavalry. You can access that digitalized record through Ancestry.com.
Also, I checked the Illinois State records (IRAD) for confirmation and it confirms the above information, with the added information of his residence as Addison, DuPage County, Illinois. Illinois has kept its civil war records and you can contact them for those records. http://www.sos.state.il.us/departments/archives/datcivil.htm...
I am one of the coordinators for Blaine NEGenWeb.