From the National Archives blog:
We first catch up with Hairy Moccasin 15 years later [after the Battle of the Little Bighorn] in an 1891 tribal census from the Census Rolls and Tribal Enumerations, 1889-1920 (NAID 1756288). He is married to Quick and the pair have two sons – Fire Head and Kills the Mud Thrower. Quick’s 70 year old mother also lives with them.
The blog continues to trace his life and even includes an image of his will.
Source: blogs.archives.gov/TextMessage/2015/05/27/life-and-times-of-hairy-moccasin/
The last paragraph of the blog has some great news for researchers: ". . . Recognizing the tremendous historical value of these records, National Archives Research Services staff across the country have been working on a multiyear project to create a new website better detailing these holdings nationwide and how to find them. To access the website and learn more information about American Indian holdings at the National Archives, check out the webpage Researching American Indians and Alaska Natives.
— Diane Merkel

The following publications contain information about Hairy Moccasin:
Article: "Custer's Crow Scouts" • Morgan City Review • 25 October 1922.
Article: "Was It Only Custer's Folly?" by Carl W. Breihan • Golden West: True Stories of the Old West • Vol. 4, No. 5 • July 1968.
Photograph: "White-Man-Runs-Him, Hairy Moccasin, Curly and Goes Ahead" • Research Review • Vol. XII, No. 1978-9 • September 1978.
Photograph: "Crow Scout Hairy Moccasin" • Research Review • Vol. XII, No. 1978-9 • September 1978.
Photograph: "Hairy Moccasin" • Research Review • Vol. XVII, No. 1983-12 • December 1983.
Article: "Curtis Photographs Offer Unique Glimpse of Custer's Crow Scouts" by James S. Brust • New view of Goes Ahead, Hairy Moccasin, and White Man Runs Him. • Greasy Grass, Journal of the Custer Battlefield Historical & Museum Association • Vol. 13 • May 1997.
Article: "Hair Moccasin's Story of the Battle: A Crow scout's account of the Battle of the Little Bighorn" by Bruce Brown • Astonisher.com • June 2006.
Article: "From Scouting for Custer to Farming the Plains: The Life and Times of Hair Moccasin as Seen in the Crow Indian Agency Records" by Cody White, Archivist at the National Archives at Denver • https://text-message.blogs.archives.gov/2015/05/27/life-and-times-of-hairy-moccasin/ • 2015.