Here's the 1910 Census for Carroll:
"United States Census, 1910," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:MKJR-DXD : accessed 19 August 2017), Carol Furgeson, Hurricane, Franklin, Arkansas, United States; citing enumeration district (ED) ED 43, sheet 5B, family 104, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 50; FHL microfilm 1,374,063.
You might also want to take a look at this 1880 Census for Carrol J. Ferguson. The middle initial is incorrect but it comes from the same county where Carroll lived at the time of his marriage. Carroll is a fairly unique given name, so this record probably deserves due consideration until it can be eliminated. From context, it identifies Mollisa (Robbins) Ferguson, a 23-year old widow born in Tennessee as his mother. Tennessee parentage for Carroll is indicated on later censuses.
"United States Census, 1880," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:MNW6-88V : 12 August 2017), Carrol J Furgison in household of William H Robbins, Reville, Logan, Arkansas, United States; citing enumeration district ED 98, sheet 276C, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 0050; FHL microfilm 1,254,050.