1930 census, Neal, Mississippi County, AR, for George W. Harrison, b. about 1887 in Alabama, working as a farmer--lists family members:
--Mamie J. Harrison, b. about 1897 in TX (wife)
--Lola/Lara M., b. about 1915 in AL (daughter)
--Odel M., b. about 1917 in AL (daughter)
--Ruby A., b. about 1919 in AR (daughter)
--Frankie L., b. about 1926 in AR (daughter)
--Thomas G., b. about 1929 in AR (son)

In 1920, listed at Marinello Road in Martin, Conway, Alabama, with wife Mayme Harrison and children Odell, Lara/Lola and Ruby (mentioned above)

There are several WW1 draft registrations for a George Washington Harrison; they do not appear to be your George, due to the names of the wives listed. They are:
--GWH, Clark County, AR, b. 29 June 1881, wife Vina (sp?) Harrison
--GWH, Coosa County, AL, b. Sep. 16, 11882, husband of Mis

There is a "George Was. Harrison" died June 13, 1937 in Mississippi County, AR, but no further identifiers for him. Likely/possibly your George, though, as he definitely lived in Mississippi County.