“Close only counts in horseshoes and hand grenades” is a saying that has been cited in print since at least 1965.
 
“Dancing” is often added to the expression. “‘But you know what they say,’ (Timmy—ed.) Hutton commented, ‘close only counts in dancing, horseshoes and hand grenade throwing’” was printed in the Spokane (WA) Daily Chronicle on June 9, 1971. “‘Close only counts in horseshoes, hand grenades and ballroom dancing,’ he (former Oklahoma Governor Dewey Bartlett—ed.) said of his defeat” was printed in the The Daily Oklahoman (Oklahoma City, OK) on July 6, 1972. “Close only counts in horseshoes, hand grenades, and slow dancing” was printed in the book Fish Fights: A Hall of Fame Quest (2001) by Bob Rich.
     
 
Newspapers.com
9 June 1971, Spokane (WA) Daily Chronicle, “Indian Losses Not Classical” by Chuck Stewart, pg. 31, col. 8:
“But you know what they say,” (Timmy—ed.) Hutton commented, “close only counts in dancing, horseshoes and hand grenade throwing.”
     
Newspapers.com
16 March 1972, Ada (OK) Weekly News, “Bartlett Begins Senate Campaign” (AP), pg. 8, cols. 5-6:
“But,” he (former Oklahoma Governor Dewey Bartlett—ed.) added, “never let it be said that I have not learned from defeat. For one thing, I’ve learned that I don’t like it—closeness only counts in horseshoes, hand grenades and ballroom dancing, but more important, I’ve learned that a Republican in Oklahoma can take nothing for granted.”
   
Newspapers.com
6 July 1972, The Daily Oklahoman (Oklahoma City, OK), “Dewey Tries New Method In Campaign,” pg. 13, col. 4:
“Close only counts in horseshoes, hand grenades and ballroom dancing,” he (former Oklahoma Governor Dewey Bartlett—ed.) said of his defeat.
 
Newspapers.com
8 August 1974, Hazleton (PA)

, “T. Dorsey’s Famed Band Is Re-Activated; Big Band Trend Gains Great Momentum” by Phil Sarno, pg. 8, cols. 4-5:
as for more young people dancing to the big band sounds now, Murray (McEachern—ed.) said “there’s an old saying that kids are finally catching on. Closeness only counts in horseshoes, hand grenades and old-fashioned dancing.”
   
Google Books
Fish Fights:
A Hall of Fame Quest
By Bob Rich
Guilford, CT: Globe Pequot Press
2001
Pg. 82:
I had thought the object was to have the bait land as close as possible to the fish, but Brewer explained that “close only counts in horseshoes, hand grenades, and slow dancing.”
   
Google Books
Quotes to Nirvana
By John Taylor Wood
Bloomington, IN: iUniverse
2010
Pg. 4:
Being close only counts in three activities: horseshoes, hand grenades and ballroom dancing.
 
Twitter
Tim Ferguson
@tphybrid
Need a vote on Sun sermon title.  A) So Close, Yet So Far B) Close Only Counts in Horseshoes, Hand Grenades & Dancing With The Stars.
1:56 PM · Jun 4, 2010·Twitterrific for iOS
   
Google Books
Stuntman!:
My Car-Crashing, Plane-Jumping, Bone-Breaking, Death-Defying Hollywood Life
By Hal Needham
New York, NY: Little, Brown
2011
Pg. ?:
Close only counts in horseshoes, hand grenades, and dancing.
 
Twitter
Herk
@ShitHerkSays
Late student: “Oh, I was close!”
Herk: “Close only counts in horseshoes, hand grenades, and dancing.”
11:13 AM · Mar 22, 2012·Twitter for iPhone
 
Twitter
Kaia Alexander
@ThisisKaia
Replying to @RoyPeterClark
Close only counts in horseshoes, hand grenades, and slow dancing
8:23 PM · Sep 11, 2019·Twitter for iPhone