There are two Civil War soldiers from Genesee County who might be from the same family, but there is no record of a David Wetherall/Witherall/Wetherald serving:

Joshua P. Wetherald/Witherall - Cpl, 23 Michigan Infantry, Co. C; died 1917, buried in Gracelawn Cemetery.

Richard C. Wetherald - Pvt., 13 Michigan Light Artillery; died 1865, buried in Pine Run Cemetery.