Whitman may be a grandson of Moses and Mary, rather than a son.

1850 census of Bath Co., Ky, district 1, enumerated 12 Aug, lists on p. 50 as family #355:
Whitman Snedegar, 39; Elizabeth, 31; William, 14; George A. (f), 11; Moses, 10; Alonzo, 8; Martha, 5; Rebecca Morgan, 50. All born in Kentucky.

1860 census of Bath Co., Ky, Owingsville, enumerated 10 Aug, lists on p. 217 family #1574:
Elizabeth Snedegar, 34; Whitman, 50, farmer; Elizabeth, 40; William, 23; Moses, 21; Alonzo, 18; Martha, 14. All born in Kentucky.

Elizabeth is probably the widow of Isaac W. Snedegar.

1870 census of Bath Co., Ky, Wyoming precinct, enumerated 13 Aug, lists on p. 82 as family #60:
Snedegar, Whitman, 57, farmer; Elizabeth, 55; Martha, 25; Anderson, Fannie, 8; Alonza, 6. All born in Ky.

Fannie and Alonzo are actually given their own dwelling and family number, 61/61, but I doubt very much they were living in a house by themselves. :) They are also listed in household 58/58 with their father. At #59 is Elizabeth Snedigar age 44 (nee Arrowsmith), widow of Isaac W. Snedegar, and at #62 is Whitman and Elizabeth’s son William.

1880 census of Bath Co., Ky, Wyoming precinct, enumerated 4 June, lists on p. 7 as family #62/64:
Snedigar, Whitman, 69, laborer, Elizabeth, 65, wife; Martha, 21, dau; Mary F., 18, granddau; Alonzo, 15, grandson. All born Ky Ky Ky.

Mary and Alonzo are children of Jonathan Anderson and George Ann Snedigar; they should be listed with the surname Anderson.