Nobody seems to know for certain.
By 1933, it was well enough known that it was used as the title of a Marx Brothers film, which also served to popularise it. The Facts on File Encyclopedia of Word and Phrase Origins speculates that it may have a connection with the big feathering strips once used by carpenters in building wooden houses, which were, the article asserts, also called 'horse feathers'. All rights reserved. Page created 8 August 1998.