“Skiing is the only sport where you can spend an arm and a leg to break an arm and a leg” is a jocular saying about skiing that has been cited in print since at least 1990 and that has appeared on many lists of skiing quotations. The authorship is unknown, but a 1998 book (below) states it’s from Henry Beard.
 
     
Google Books
The American Legion
Volume 118, Issues 1-6
1985 (Google Books date may be incorrect—ed.)
Pg. 62:
Skiing is the sport that requires you to spend an arm and a leg to break an arm and a leg.
 
28 September 1990, Daily Republican-Register (Mt, Carmel, IL), “The Light Touch” by Dave Fithian of Kozy Karpet, pg. 16, col. 1 ad:
Skiing is the only sport in the world that requires you to spend an arm and a leg to break an arm and a leg.
   
Google Books
Little Giant Encyclopedia:
Toasts & Quotes
by Jane Johnson, Richard Hummerstone, Bruce Robertson, Diagram Group
New York, NY: Sterling Pub.
1998
Pg. 430:
Skiing is the only sport where you can spend an arm and a leg to break an arm and a leg.
HENRY BEARD
 
TheSkiDiva.com
Skiing is the only sport where you spend an arm and a leg to break an arm and a leg. ~Author Unknown
dloveski, Apr 7, 2008
 
The Ski Channel
Great all time ski quotes
Posted By: Glenn Steinbaum on October 13, 2009 5:11 pm
(...)
Skiing is the only sport where you spend an arm and a leg to break an arm and a leg.  ~Author Unknown
   
Google Books
It’s All Part of the Alpine Experience
By John B. McGrath
Bloomington, IN: AuthorHouse
2010
Pg. 135:
“Skiing is the only sport where you spend an arm and a leg to break an arm and a leg.”
Anon