Several members of the Grim/m family served during the Civil War. All that I have found at this time served for the Union. Below you can see who they were and units they served with. I have pension applications for several of them. By following the links below, you will be able to see scans of those files. The first few people listed served in the war, but I do not have their pension records.
Cooper, Reese (ca 1834-Aug. 19, 1864),
son of Uriah & Sarah Cooper and husband of Clarissa Grim; Co. D, 11th WV Infantry
Grim, David Crockett (Apr. 5, 1836-Aug. 24, 1908),
son of John Grim & Jane Grandon; Co. F, 6th WV Infantry?
Grim, Lawrence Clark (Sep. 24, 1843-Dec. 21, 1903),
son of Harvey Grim & Permelia Headley; Private, Co. G, 18th Pennsylvania Cavalry